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Journal articles on the topic 'Spherical maximal functions'

Author: Grafiati

Published: 6 September 2023

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1

Lacey, Michael T. "Sparse bounds for spherical maximal functions." Journal d'Analyse Mathématique 139, no. 2 (2019): 613–35. http://dx.doi.org/10.1007/s11854-019-0070-2.

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2

Seeger, Andreas, Stephen Wainger, and James Wright. "Spherical Maximal Operators on Radial Functions." Mathematische Nachrichten 187, no. 1 (1997): 241–65. http://dx.doi.org/10.1002/mana.19971870112.

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3

Duoandikoetxea, Javier, Adela Moyua, and Osane Oruetxebarria. "The spherical maximal operator on radial functions." Journal of Mathematical Analysis and Applications 387, no. 2 (2012): 655–66. http://dx.doi.org/10.1016/j.jmaa.2011.09.028.

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4

Kajima, Yasuhiro. "Spherical functions on orthogonal groups." Nagoya Mathematical Journal 141 (March 1996): 157–82. http://dx.doi.org/10.1017/s0027763000005572.

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Let G be a p-adic connected reductive algebraic group and K a maximal compact subgroup of G. In [4], Casselman obtained the explicit formula of zonal spherical functions on G with respect to K on the assumption that K is special. It is known (Bruhat and Tits [3]) that the affine root system of algebraic group which has good but not special maximal compact subgroup is A1 C2, or Bn (n > 3), and all Bn-types can be realized by orthogonal groups. Here the assumption “good” is necessary for the Satake’s theory of spherical functions.

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5

Kesler, Robert, Michael T. Lacey, and Darío Mena. "Sparse bounds for the discrete spherical maximal functions." Pure and Applied Analysis 2, no. 1 (2020): 75–92. http://dx.doi.org/10.2140/paa.2020.2.75.

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6

Gauthier, P. M., and J. Xiao. "Functions of bounded expansion: normal and Bloch functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 66, no. 2 (1999): 168–88. http://dx.doi.org/10.1017/s144678870003929x.

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AbstractNormal functions and Bloch functions are respectively functions of bounded spherical expansion and bounded Euclidean expansion. In this paper we discuss the behaviour of normal functions and of Bloch functions in terms of the maximal ideal space of H∞, the Bergman projection and the Ahlfors-Shimizu characteristic.

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7

Roos, Joris, and Andreas Seeger. "Spherical maximal functions and fractal dimensions of dilation sets." American Journal of Mathematics 145, no. 4 (2023): 1077–110. http://dx.doi.org/10.1353/ajm.2023.a902955.

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abstract: For the spherical mean operators $\scr{A}_t$ in $\Bbb{R}^d$, $d\ge 2$, we consider the maximal functions $M_Ef=\sup_{t\in E}|\scr{A}_t f|$, with dilation sets $E\subset [1,2]$. In this paper we give a surprising characterization of the closed convex sets which can occur as closure of the sharp $L^p$ improving region of $M_E$ for some $E$. This region depends on the Minkowski dimension of $E$, but also other properties of the fractal geometry such as the Assouad spectrum of $E$ and subsets of $E$. A key ingredient is an essentially sharp result on $M_E$ for a class of sets called (qua

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8

Anderson, Theresa C., and Eyvindur Ari Palsson. "Bounds for discrete multilinear spherical maximal functions in higher dimensions." Bulletin of the London Mathematical Society 53, no. 3 (2021): 855–60. http://dx.doi.org/10.1112/blms.12465.

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Dosidis, Georgios, and Loukas Grafakos. "On families between the Hardy–Littlewood and spherical maximal functions." Arkiv för Matematik 59, no. 2 (2021): 323–43. http://dx.doi.org/10.4310/arkiv.2021.v59.n2.a4.

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10

Leckband, Mark. "A note on the spherical maximal operator for radial functions." Proceedings of the American Mathematical Society 100, no. 4 (1987): 635. http://dx.doi.org/10.1090/s0002-9939-1987-0894429-9.

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11

Cowling, Michael, José García-Cuerva, and Hendra Gunawan. "Weighted estimates for fractional maximal functions related to spherical means." Bulletin of the Australian Mathematical Society 66, no. 1 (2002): 75–90. http://dx.doi.org/10.1017/s0004972700020694.

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We prove weighted Lp-Lq estimates for the maximal operators ℳα, given by , where μt denotes the normalised surface measure on the sphere of centre 0 and radius t in Rd. The techniques used involve interpolation and the Mellin transform. To do this, we also prove weighted Lp-Lq estimates for the operators of convolution with the kernels |·|−α−iη.

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12

Ho, Kwok-Pun. "Spherical maximal functions, variation and oscillation inequalities on Herz spaces." Arab Journal of Basic and Applied Sciences 26, no. 1 (2019): 72–77. http://dx.doi.org/10.1080/25765299.2018.1554201.

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13

Hughes, Kevin. "Restricted weak-type endpoint estimates for k-spherical maximal functions." Mathematische Zeitschrift 286, no. 3-4 (2017): 1303–21. http://dx.doi.org/10.1007/s00209-016-1802-y.

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14

Deleaval, Luc. "On the boundedness of the Dunkl spherical maximal operator." Journal of Topology and Analysis 08, no. 03 (2016): 475–95. http://dx.doi.org/10.1142/s1793525316500163.

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In this paper, we introduce a Dunkl-type spherical maximal operator associated with a finite reflection group and study its boundedness. In view of this study, we give some results on suitable square functions and maximal multiplier operators in the Dunkl setting.

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15

Flicker, Yuval Z. "Stable base change for spherical functions." Nagoya Mathematical Journal 106 (June 1987): 121–42. http://dx.doi.org/10.1017/s0027763000000921.

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Let E/F be an unramified cyclic extension of local non-archimedean fields, G a connected reductive group over F, K(F) (resp. K(E)) a hyper-special maximal compact subgroup of G(F) (resp. G(E)), and H(F) (resp. H(E)) the Hecke convolution algebra of compactly-supported complex-valued K(F) (resp. G(E))-biinvariant functions on G(F) (resp. G(E)). Then the theory of the Satake transform defines (see § 2) a natural homomorphism H(E) → H(F), θ→f. There is a norm map N from the set of stable twisted conjugacy classes in G(E) to the set of stable conjugacy classes in G(F); it is an injection (see [Ko]

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16

Ciaurri, Óscar, Adam Nowak, and Luz Roncal. "Maximal estimates for a generalized spherical mean Radon transform acting on radial functions." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 4 (2019): 1597–619. http://dx.doi.org/10.1007/s10231-019-00933-x.

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17

Romera, Elena, and Fernando Soria. "Endpoint estimates for the maximal operator associated to spherical partial sums on radial functions." Proceedings of the American Mathematical Society 111, no. 4 (1991): 1015. http://dx.doi.org/10.1090/s0002-9939-1991-1068130-6.

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18

LARSEN, NADIA S., and RUI PALMA. "Positive definite *-spherical functions, property (T) and C*-completions of Gelfand pairs." Mathematical Proceedings of the Cambridge Philosophical Society 160, no. 1 (2015): 77–93. http://dx.doi.org/10.1017/s0305004115000559.

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AbstractThe study of existence of a universal C*-completion of the *-algebra canonically associated to a Hecke pair was initiated by Hall, who proved that the Hecke algebra associated to (SL2($\mathbb{Q}$p), SL2($\mathbb{Z}$p)) does not admit a universal C*-completion. Kaliszewski, Landstad and Quigg studied the problem by placing it in the framework of Fell–Rieffel equivalence, and highlighted the role of other C*-completions. In the case of the pair (SLn($\mathbb{Q}$p), SLn($\mathbb{Z}$p)) for n ⩾ 3 we show, invoking property (T) of SLn($\mathbb{Q}$p), that the C*-completion of the L1-Banach

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19

Andersen, Kenneth F. "Weighted inequalities for the Stieltjes transform and the maximal spherical partial sum operator on radial functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 1 (1995): 195–204. http://dx.doi.org/10.1017/s0308210500030833.

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If TRf(x) is the spherical partial sum of the Fourier transform of f and T*f(x) = SUPR > 0 | TRf(x)|, sufficient conditions are given on the non-negative weight function ω(x) which ensure that T* restricted to radial functionsis bounded on the Lorentz space Lp,s(Rn,ω) into Lp,q(Rn, ω) For power weights, these conditions are also necessary. The weight pairs (u,v) for which the generalised Stieltjes transform Sλ is bounded from LP,S(R+, v)into Lp,q(R+, u)are also characterised. These are an essential ingredient for the study of T*.

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20

Cartwright, Donald I., and Wojciech MŁotkowski. "Harmonic analysis for groups acting on triangle buildings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 56, no. 3 (1994): 345–83. http://dx.doi.org/10.1017/s1446788700035540.

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AbstractLet Δ be a thick building of type Ã2, and let be its set of vertices. We study a commutative algebra of ‘averaging’ operators acting on the space of complex valued functions on . This algebra may be identified with a space of ‘biradial functions’ on , or with a convolution algebra of bi-K-invariant functions on G, if G is a sufficiently large group of ‘type-rotating’ automorphisms of Δ, and K is the subgroup of G fixing a given vertex. We describe the multiplicative functionals on and the corresponding spherical functions. We consider the C*-algebra induced by on l2, find its spectrum

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21

Garrigós, Gustavo, and Andreas Seeger. "On plate decompositions of cone multipliers." Proceedings of the Edinburgh Mathematical Society 52, no. 3 (2009): 631–51. http://dx.doi.org/10.1017/s001309150700048x.

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AbstractAn important inequality due to Wolff on plate decompositions of cone multipliers is known to have consequences for sharp Lp results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones, averages over finite-type curves in ℝ3 and associated maximal functions. We observe that the range of p in Wolff's inequality, for the conic and the spherical versions, can be improved by using bilinear restriction results. We also use this inequality to give some improved estimates on square functions associated to decompo

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22

Benavides-Bravo, Francisco Gerardo, Roberto Soto-Villalobos, José Roberto Cantú-González, Mario A. Aguirre-López, and Ángela Gabriela Benavides-Ríos. "A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series." Mathematics 9, no. 19 (2021): 2466. http://dx.doi.org/10.3390/math9192466.

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Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally pro

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23

Mason-Brown, Lucas. "Regular Functions on the 𝐾-nilpotent cone". Representation Theory of the American Mathematical Society 26, № 33 (2022): 1047–62. http://dx.doi.org/10.1090/ert/629.

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Let G G be a complex reductive algebraic group with Lie algebra g \mathfrak {g} and let G R G_{\mathbb {R}} be a real form of G G with maximal compact subgroup K R K_{\mathbb {R}} . Associated to G R G_{\mathbb {R}} is a K × C × K \times \mathbb {C}^{\times } -invariant subvariety N θ \mathcal {N}_{\theta } of the (usual) nilpotent cone N ⊂ g ∗ \mathcal {N} \subset \mathfrak {g}^* . In this article, we will derive a formula for the ring of regular functions C [ N θ ] \mathbb {C}[\mathcal {N}_{\theta }] as a representation of K × C × K \times \mathbb {C}^{\times } . Some motivation comes from H

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24

Lakzian, Sajjad, and Michael Munn. "On Weak Super Ricci Flow through Neckpinch." Analysis and Geometry in Metric Spaces 9, no. 1 (2021): 120–59. http://dx.doi.org/10.1515/agms-2020-0123.

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Abstract In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost functions which are increasing convex functions of the distance function). Our definition of a weak super Ricci flow is based on the coupled contraction property for suitably defined diffusions on maximal diffusion subspaces. In our main theorem, we show that if a non-degenerate spherical neckpinch can be continued beyond the singular time by a smoo

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25

Ahrens, Cory, and Gregory Beylkin. "Rotationally invariant quadratures for the sphere." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2110 (2009): 3103–25. http://dx.doi.org/10.1098/rspa.2009.0104.

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We construct near-optimal quadratures for the sphere that are invariant under the icosahedral rotation group. These quadratures integrate all ( N +1) 2 linearly independent functions in a rotationally invariant subspace of maximal order and degree N . The nodes of these quadratures are nearly uniformly distributed, and the number of nodes is only marginally more than the optimal ( N +1) 2 /3 nodes. Using these quadratures, we discretize the reproducing kernel on a rotationally invariant subspace to construct an analogue of Lagrange interpolation on the sphere. This representation uses function

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26

Lemaire, Bertrand, and Manish Mishra. "Matching of orbital integrals (transfer) and Roche Hecke algebra isomorphisms." Compositio Mathematica 156, no. 3 (2020): 533–603. http://dx.doi.org/10.1112/s0010437x19007838.

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Let $F$ be a non-Archimedean local field, $G$ a connected reductive group defined and split over $F$, and $T$ a maximal $F$-split torus in $G$. Let $\unicode[STIX]{x1D712}_{0}$ be a depth-zero character of the maximal compact subgroup $T$ of $T(F)$. This gives by inflation a character $\unicode[STIX]{x1D70C}$ of an Iwahori subgroup $\unicode[STIX]{x2110}\subset T$ of $G(F)$. From Roche [Types and Hecke algebras for principal series representations of split reductive$p$-adic groups, Ann. Sci. Éc. Norm. Supér. (4) 31 (1998), 361–413], $\unicode[STIX]{x1D712}_{0}$ defines a reductive $F$-split gr

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27

Kulikov, A. N., E. V. Kudryashova, P. P. Mikhailov, and A. R. Suleimanova. "Intrastromal keratoplasty with intracorneal ring segments implantation as an independent method of visual rehabilitation in patients with keratoconus." Modern technologies in ophtalmology, no. 5 (October 20, 2021): 137–42. http://dx.doi.org/10.25276/2312-4911-2021-5-137-142.

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Purpose. To assess the possibility of using intrastromal keratoplasty with intracorneal ring segments implantation as an independent technique to achieve visual rehabilitation in patients with keratoconus of the stages I and II. Material and methods. There were examined and operated 14 eyes (10 patients) with keratoconus of the stages I and II (classification by Izmailova SB, 2014). Patients were divided into two groups depending on the keratoconus stage. All patients underwent intrastromal keratoplasty with intracorneal ring segments implantation using the femtosecond technology. The on avera

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28

Goldshtein, A., M. SHAPIRO, and C. Gutfinger. "Mechanics of collisional motion of granular materials. Part 3. Self-similar shock wave propagation." Journal of Fluid Mechanics 316 (June 10, 1996): 29–51. http://dx.doi.org/10.1017/s0022112096000432.

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Shock wave propagation arising from steady one-dimensional motion of a piston in a granular gas composed of inelastically colliding particles is treated theoretically. A self-similar long-time solution is obtained in the strong shock wave approximation for all values of the upstream gas volumetric concentration v0. Closed form expressions for the long-time shock wave speed and the granular pressure on the piston are obtained. These quantities are shown to be independent of the particle collisional properties, provided their impacts are accompanied by kinetic energy losses. The shock wave speed

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29

Bain, Gregory, Tom McNaughton, Ruth Williams, and Simon MacLean. "Microstructure of the Distal Radius and Its Relevance to Distal Radius Fractures." Journal of Wrist Surgery 06, no. 04 (2017): 307–15. http://dx.doi.org/10.1055/s-0037-1602849.

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Background There is a paucity of information on the microstructure of the distal radius, and how this relates to its morphology and function. Purpose This study aims to assess the microanatomical structure of the distal radius, and relate this to its morphology, function, and modes of failure. Methods Six dry adult skeletal distal radii were examined with microcomputed tomography scan and analyzed with specialist computer software. From 3D and 2D images, the subchondral, cortical, and medullary trabecular were assessed and interpreted based on the overall morphology of the radius. Results The

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30

Escassut, Alain. "The Ultrametric Corona Problem and spherically complete fields." Proceedings of the Edinburgh Mathematical Society 53, no. 2 (2010): 353–71. http://dx.doi.org/10.1017/s0013091508000837.

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AbstractLet K be a complete ultrametric algebraically closed field and let A be the Banach K-algebra of bounded analytic functions in the ‘open’ unit disc D of K provided with the Gauss norm. Let Mult(A,‖ · ‖) be the set of continuous multiplicative semi-norms of A provided with the topology of simple convergence, let Multm(A, ‖ · ‖) be the subset of the φ ∈ Mult(A, ‖ · ‖) whose kernel is a maximal ideal and let Multa(A, ‖ · ‖) be the subset of the φ ∈ Mult(A, ‖ · ‖) whose kernel is a maximal ideal of the form (x − a)A with a ∈ D. We complete the characterization of continuous multiplicative n

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31

Noda, Yohei, Satoshi Koizumi, Tomomi Masui, et al. "Contrast variation by dynamic nuclear polarization and time-of-flight small-angle neutron scattering. I. Application to industrial multi-component nanocomposites." Journal of Applied Crystallography 49, no. 6 (2016): 2036–45. http://dx.doi.org/10.1107/s1600576716016472.

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Dynamic nuclear polarization (DNP) at low temperature (1.2 K) and high magnetic field (3.3 T) was applied to a contrast variation study in small-angle neutron scattering (SANS) focusing on industrial rubber materials. By varying the scattering contrast by DNP, time-of-flight SANS profiles were obtained at the pulsed neutron source of the Japan Proton Accelerator Research Complex (J-PARC). The concentration of a small organic molecule, (2,2,6,6-tetramethylpiperidine-1-yl)oxy (TEMPO), was carefully controlled by a doping method using vapour sorption into the rubber specimens. With the assistance

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32

Roncal, Luz, Saurabh Shrivastava, and Kalachand Shuin. "Bilinear Spherical Maximal Functions of Product Type." Journal of Fourier Analysis and Applications 27, no. 4 (2021). http://dx.doi.org/10.1007/s00041-021-09877-4.

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33

Anderson, Theresa C., and Eyvindur Ari Palsson. "Bounds for discrete multilinear spherical maximal functions." Collectanea Mathematica, January 3, 2021. http://dx.doi.org/10.1007/s13348-020-00308-z.

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34

Anderson, Theresa C., Brian Cook, Kevin Hughes та Angel Kumchev. "Improved ℓp -Boundedness for Integral k -Spherical Maximal Functions". Discrete Analysis, 29 травня 2018. http://dx.doi.org/10.19086/da.3675.

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35

Roos, Joris, Andreas Seeger, and Rajula Srivastava. "Lebesgue Space Estimates for Spherical Maximal Functions on Heisenberg Groups." International Mathematics Research Notices, September 11, 2021. http://dx.doi.org/10.1093/imrn/rnab246.

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Abstract We prove $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups; these are sharp up to two endpoints. The results can be applied to improve currently known bounds on sparse domination for global maximal operators. We also consider lacunary variants and extensions to Métivier groups.

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36

Nowak, Adam, Luz Roncal, and Tomasz Z. Szarek. "Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions." Communications on Pure and Applied Analysis, 2023, 0. http://dx.doi.org/10.3934/cpaa.2023065.

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37

Makinde, Olusola S. "Depth classification based on affine-invariant, weighted and kernel-based spatial depth functions." Kuwait Journal of Science 48, no. 2 (2021). http://dx.doi.org/10.48129/kjs.v48i2.8693.

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Several multivariate depth functions have been proposed in the literature, of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. The covariance-adjusted, weighted, and kernel-based versions of spatial depth functions are presented to classify multivariate outcomes. We extend the maximal depth classification notions for the covariance-adjusted, weighted, and kernel-based s

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38

Zienkiewicz-Strzałka, Małgorzata, Anna Deryło-Marczewska, and Stanisław Pikus. "The synthesis and nanostructure investigation of noble metal-based nanocomposite materials." Journal of Materials Science, May 6, 2021. http://dx.doi.org/10.1007/s10853-021-06127-2.

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AbstractThe presented work follows the theme of applied chemistry toward nanomaterials and multiphase functional systems of practical importance. Structural studies of nanocomposite materials are important due to the correlation between physicochemical/structural properties and their application potential. In this work, we report the fabrication and structural characterization of nanocomposite materials constituting noble metal (plasmonic) nanoparticles (AgNP and AuNP) dispersed on selected types of nanostructured solid hosts (nonporous silica, microporous activated carbon, chitosan biopolymer

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Dalal, Kesha, Venkatesh Katari, Sailaja Paruchuri, and Charles Thodeti. "Regulation of endothelial cell mitochondrial phenotype by mechanosensitive ion channel TRPV4." Physiology 38, S1 (2023). http://dx.doi.org/10.1152/physiol.2023.38.s1.5732666.

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Transient receptor potential vanilloid type 4 (TRPV4) is a mechanosensor that regulates endothelial cell (EC) proliferation, migration, and angiogenesis. However, the molecular mechanisms by which TRPV4 regulates EC functions are not well understood. In this study, we investigated if TRPV4 regulates EC function via modulation of mitochondria by employing three types of EC expressing different levels of TRPV4, normal (NEC), TRPV4-deficienct (TEC), and TRPV4 knockout (KOEC). First, we confirmed the functional expression of TRPV4 in these EC using qPCR and calcium imaging. Confocal images upon Mi

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40

Bruno, Nicholas. "Ideal structure of rings of analytic functions with non-Archimedean metrics." Journal of Algebra and Its Applications, October 14, 2021. http://dx.doi.org/10.1142/s0219498823500111.

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The work of Helmer [Divisibility properties of integral functions, Duke Math. J. 6(2) (1940) 345–356] applied algebraic methods to the field of complex analysis when he proved the ring of entire functions on the complex plane is a Bezout domain (i.e. all finitely generated ideals are principal). This inspired the work of Henriksen [On the ideal structure of the ring of entire functions, Pacific J. Math. 2(2) (1952) 179–184. On the prime ideals of the ring of entire functions, Pacific J. Math. 3(4) (1953) 711–720] who proved a correspondence between the maximal ideals within the ring of entire

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41

Brassel, Byron P., Sunil D. Maharaj, and Rituparno Goswami. "Charged radiation collapse in Einstein–Gauss–Bonnet gravity." European Physical Journal C 82, no. 4 (2022). http://dx.doi.org/10.1140/epjc/s10052-022-10334-9.

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AbstractWe generalise the continual gravitational collapse of a spherically symmetric radiation shell of matter in five dimensional Einstein–Gauss–Bonnet gravity to include the electromagnetic field. The presence of charge has a significant effect in the collapse dynamics. We note that there exists a maximal charge contribution for which the metric functions in Einstein–Gauss–Bonnet gravity remain real, which is not the case in general relativity. Beyond this maximal charge the spacetime metric is complex. The final fate of collapse for the uncharged matter field, with positive mass, is an ext

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42

Brassel, Byron P., Sunil D. Maharaj, and Rituparno Goswami. "Charged radiation collapse in Einstein–Gauss–Bonnet gravity." European Physical Journal C 82, no. 4 (2022). http://dx.doi.org/10.1140/epjc/s10052-022-10334-9.

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AbstractWe generalise the continual gravitational collapse of a spherically symmetric radiation shell of matter in five dimensional Einstein–Gauss–Bonnet gravity to include the electromagnetic field. The presence of charge has a significant effect in the collapse dynamics. We note that there exists a maximal charge contribution for which the metric functions in Einstein–Gauss–Bonnet gravity remain real, which is not the case in general relativity. Beyond this maximal charge the spacetime metric is complex. The final fate of collapse for the uncharged matter field, with positive mass, is an ext

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