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Journal articles on the topic 'Carleson measure'

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Published: 4 June 2021
Last updated: 28 January 2023

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1

Bernstein, S., and P. Cerejeiras. "Carleson measure and monogenic functions." Studia Mathematica 180, no. 1 (2007): 11–25. http://dx.doi.org/10.4064/sm180-1-2.

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2

Xiao, Jie. "The Qp Carleson measure problem." Advances in Mathematics 217, no. 5 (March 2008): 2075–88. http://dx.doi.org/10.1016/j.aim.2007.08.015.

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3

Heiming, Helmut J. "Carleson embeddings." Abstract and Applied Analysis 1, no. 2 (1996): 193–201. http://dx.doi.org/10.1155/s1085337596000097.

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In this paper we discuss several operator ideal properties for so called Carleson embeddings of tent spaces into specificL q(μ)-spaces, whereμis a Carleson measure on the complex unit disc. Characterizing absolutelyq-summing, absolutely continuous andq-integral Carleson embeddings in terms of the underlying measure is our main topic. The presented results extend and integrate results especially known for composition operators on Hardy spaces as well as embedding theorems for function spaces of similar kind.
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4

Wu, Xinfeng. "Weighted Carleson Measure Spaces Associated with Different Homogeneities." Canadian Journal of Mathematics 66, no. 6 (December 1, 2014): 1382–412. http://dx.doi.org/10.4153/cjm-2013-021-1.

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AbstractIn this paper, we introduce weighted Carleson measure spaces associated with different homogeneities and prove that these spaces are the dual spaces of weighted Hardy spaces studied in a forthcoming paper. As an application, we establish the boundedness of composition of two Calderón–Zygmund operators with different homogeneities on the weighted Carleson measure spaces; this, in particular, provides the weighted endpoint estimates for the operators studied by Phong–Stein.
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5

Liu, Junming, and Zengjian Lou. "Carleson measure for analytic Morrey spaces." Nonlinear Analysis 125 (September 2015): 423–32. http://dx.doi.org/10.1016/j.na.2015.05.016.

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6

Zengjian, Lou. "Carleson measure characterization of Bloch functions." Acta Mathematica Sinica 12, no. 2 (June 1996): 175–84. http://dx.doi.org/10.1007/bf02108160.

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7

LEE, MING-YI, and CHIN-CHENG LIN. "CARLESON MEASURE SPACES ASSOCIATED TO PARA-ACCRETIVE FUNCTIONS." Communications in Contemporary Mathematics 14, no. 01 (February 2012): 1250002. http://dx.doi.org/10.1142/s0219199712500022.

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To study the boundedness of the Cauchy integrals over Lipschitz curves, new Hardy spaces [Formula: see text] were introduced in [Y. Han, M.-Y. Lee and C.-C. Lin, Hardy spaces and the Tb theorem, J. Geom. Anal.14 (2004) 291–318], where b is a para-accretive function. In this paper, we define the Carleson measure spaces [Formula: see text] that generalize BMO, and show that [Formula: see text] is the dual space of [Formula: see text]. As an application, we give a Carleson measure characterization of BMOb.
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8

Zhao, Kai. "Carleson Measure and Tent Spaces on the Siegel Upper Half Space." Abstract and Applied Analysis 2012 (2012): 1–23. http://dx.doi.org/10.1155/2012/583156.

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The Hausdorff capacity on the Heisenberg group is introduced. The Choquet integrals with respect to the Hausdorff capacity on the Heisenberg group are defined. Then the fractional Carleson measures on the Siegel upper half space are discussed. Some characterized results and the dual of the fractional Carleson measures on the Siegel upper half space are studied. Therefore, the tent spaces on the Siegel upper half space in terms of the Choquet integrals are introduced and investigated. The atomic decomposition and the dual spaces of the tent spaces are obtained at the last.
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9

David, Guy, Linhan Li, and Svitlana Mayboroda. "Carleson Measure Estimates for the Green Function." Archive for Rational Mechanics and Analysis 243, no. 3 (January 28, 2022): 1525–63. http://dx.doi.org/10.1007/s00205-021-01746-0.

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10

Liu, Hsun-Wu, and Kunchuan Wang. "A Characterization of Weighted Carleson Measure Spaces." Taiwanese Journal of Mathematics 23, no. 1 (February 2019): 103–27. http://dx.doi.org/10.11650/tjm/180408.

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11

Lin, Chin-Cheng, and Kunchuan Wang. "Generalized Carleson Measure Spaces and Their Applications." Abstract and Applied Analysis 2012 (2012): 1–26. http://dx.doi.org/10.1155/2012/879073.

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We introduce the generalized Carleson measure spaces CMOrα,qthat extend BMO. Using Frazier and Jawerth'sφ-transform and sequence spaces, we show that, forα∈Rand0<p≤1, the duals of homogeneous Triebel-Lizorkin spacesḞpα,qfor1<q<∞and0<q≤1are CMO(q'/p)-(q'/q)-α,q'and CMOr-α+(n/p)-n,∞(for anyr∈R), respectively. As applications, we give the necessary and sufficient conditions for the boundedness of wavelet multipliers and paraproduct operators acting on homogeneous Triebel-Lizorkin spaces.
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12

Jevtić, Miroljub. "Two Carleson measure theorems for Hardy spaces." Indagationes Mathematicae (Proceedings) 92, no. 3 (September 1989): 315–21. http://dx.doi.org/10.1016/s1385-7258(89)80006-x.

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13

Yang, Weisheng. "Carleson type measure characterization of Qp spaces." Analysis 18, no. 4 (December 1998): 345–50. http://dx.doi.org/10.1524/anly.1998.18.4.345.

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14

Huang, Jizheng, Mingshuang Duan, Yaqiong Wang, and Weiwei Li. "Fractional Carleson measure associated with Hermite operator." Analysis and Mathematical Physics 9, no. 4 (April 17, 2019): 2075–97. http://dx.doi.org/10.1007/s13324-019-00300-2.

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15

Choa, Jun Soo. "A property of series of holomorphic homogeneous polynomials with Hadamard gaps." Bulletin of the Australian Mathematical Society 53, no. 3 (June 1996): 479–84. http://dx.doi.org/10.1017/s000497270001724x.

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Recently J. Miao proved that if is a holomorphic function with Hadamard gaps on the open unit disc D then f ∈ Xp if and only if f ∈ Bp if and only if if and if only if where Xp, Bp and denote respectively the class of holomorphic functions on D which satisfy |f′(z)|p(1 − |z|2)p − 1dxdy is a finite measure, a Carleson measure and a little Carleson measure on D. In this paper we give a higher-dimensional version of Miao's result.
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16

Power, S. C. "Hörmander's Carleson theorem for the ball." Glasgow Mathematical Journal 26, no. 1 (January 1985): 13–17. http://dx.doi.org/10.1017/s0017089500005711.

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Let denote the unit ball in ℂ2 and let Sdenote its boundary, the unit sphere. For z ∈ B and δ>0, the following non isotropic balls are defined, where A finite positive Borel measure μ, on B is called a Carleson measure if there exists a constant C for whichHere σ denotes normalized surface area measure on S. The following theorem was obtained by Hörmander [6] as a special case of more general variants for strictly pseudoconvex domains in ℂn. Recently Cima and Wogen [3] derived it from a Carleson measure theorem for Bergman spaces of the ball. A different direct approach to the Bergman context, and related settings, is given in Leucking [7].
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17

Kang, Hyeonbae, and Hyungwoon Koo. "Carleson measure characterizations of BMOA on pseudoconvex domains." Pacific Journal of Mathematics 178, no. 2 (April 1, 1997): 279–91. http://dx.doi.org/10.2140/pjm.1997.178.279.

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18

Wang, Jianfei. "The Carleson Measure Problem Between Analytic Morrey Spaces." Canadian Mathematical Bulletin 59, no. 4 (December 1, 2016): 878–90. http://dx.doi.org/10.4153/cmb-2016-013-9.

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AbstractThe purpose of this paper is to characterize positive measure μ on the unit disk such that the analytic Morrey space is boundedly and compactly embedded to the tent spacefor the case 1 ≤ q ≤ p ∞ respectively. As an application, these results are used to establish the boundedness and compactness of integral operators and multipliers between analytic Morrey spaces.
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19

Gu, Dangsheng. "A carleson measure theorem for weighted bergman spaces." Complex Variables, Theory and Application: An International Journal 21, no. 1-2 (February 1993): 79–86. http://dx.doi.org/10.1080/17476939308814616.

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20

Hansen, S. "New results on the operator Carleson measure criterion." IMA Journal of Mathematical Control and Information 14, no. 1 (March 1, 1997): 3–32. http://dx.doi.org/10.1093/imamci/14.1.3.

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21

Xu, An-Jian, and Zou Yang. "Carleson Measure in Bergman-Orlicz Space of Polydisc." Abstract and Applied Analysis 2010 (2010): 1–7. http://dx.doi.org/10.1155/2010/603968.

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Letμbe a finite, positive measure on&#x1D53B;n, the polydisc inℂn, and letσnbe 2n-dimensional Lebesgue volume measure on&#x1D53B;n. For an Orlicz functionφ, a necessary and sufficient condition onμis given in order that the identity mapJ:Laφ(&#x1D53B;n,σn)→Lφ(&#x1D53B;n,μ)is bounded.
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22

Hu, Guangming, Yutong Liu, Yu Sun, and Xinjie Qian. "Carleson Measure of Harmonic Schwarzian Derivatives Associated with a Finitely Generated Fuchsian Group of the Second Kind." Journal of Function Spaces 2021 (March 20, 2021): 1–6. http://dx.doi.org/10.1155/2021/5523454.

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Let S H f be the Schwarzian derivative of a univalent harmonic function f in the unit disk D , compatible with a finitely generated Fuchsian group G of the second kind. We show that if S H f 2 1 − z 2 3 d x d y satisfies the Carleson condition on the infinite boundary of the Dirichlet fundamental domain F of G , then S H f 2 1 − z 2 3 d x d y is a Carleson measure in D .
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23

El-Sayed Ahmed, A., and M. A. Bakhit. "Composition operators on some holomorphic Banach function spaces." MATHEMATICA SCANDINAVICA 104, no. 2 (June 1, 2009): 275. http://dx.doi.org/10.7146/math.scand.a-15098.

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In this paper, we study composition operators on some Möbius invariant Banach function spaces like Bloch and $F(p,q,s)$ spaces. We give a Carleson measure characterization on $F(p,q,s)$ spaces, then we use this Carleson measure characterization of the compact compositions on $F(p,q,s)$ spaces to show that every compact composition operator on $F(p,q,s)$ spaces is compact on a Bloch space. Also, we give conditions to clarify when the converse holds.
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24

Miao, Jie. "Characterisations for analytic functions of bounded mean oscillation." Bulletin of the Australian Mathematical Society 46, no. 1 (August 1992): 115–25. http://dx.doi.org/10.1017/s0004972700011722.

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Let α > 0 and let f[α](z) be the αth fractional derivative of an analytic function f on the unit disc D. In this paper we show that f ∈ BMOA if and only if |f[α](z)|2 (l - |z|2)2α−1dA(z) is a Carleson measure and f ∈ VMOA if and only if |f[α](z)|2 (1 − |z|2)2α−1dA(z) is a vanishing Carleson measure, where A denotes the normalised Lebesgue measure on D. Hence a significant extension of familiar characterisations for analytic functions of bounded and vanishing mean oscillation is obtained.
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25

CHUNG, YONG MOO, and HIROKI TAKAHASI. "Multifractal formalism for Benedicks–Carleson quadratic maps." Ergodic Theory and Dynamical Systems 34, no. 4 (March 11, 2013): 1116–41. http://dx.doi.org/10.1017/etds.2012.188.

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AbstractFor a positive measure set of non-uniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given continuous function and consider the associated Birkhoff spectrum which encodes this decomposition. We derive a formula which relates the Hausdorff dimension of level sets to entropies and Lyapunov exponents of invariant probability measures, and then use this formula to show that the spectrum is continuous. In order to estimate the Hausdorff dimension from above, one has to ‘see’ sufficiently many points. To this end, we construct a family of towers. Using these towers we establish a large deviation principle of empirical distributions, with Lebesgue as a reference measure.
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26

Sundhäll, Marcus, and Edgar Tchoundja. "On Hankel Forms of Higher Weights: The Case of Hardy Spaces." Canadian Journal of Mathematics 62, no. 2 (April 1, 2010): 439–55. http://dx.doi.org/10.4153/cjm-2010-027-8.

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AbstractIn this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by Sundh¨all for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.
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27

Aleman, Alexandru, Michael Hartz, John E. McCarthy, and Stefan Richter. "Interpolating Sequences in Spaces with the Complete Pick Property." International Mathematics Research Notices 2019, no. 12 (October 12, 2017): 3832–54. http://dx.doi.org/10.1093/imrn/rnx237.

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Abstract We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This generalizes results of Carleson for the Hardy space and of Bishop, Marshall, and Sundberg for the Dirichlet space. Furthermore, we investigate interpolating sequences for pairs of Hilbert function spaces.
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28

Bishop, Christopher. "Conformal images of Carleson curves." Proceedings of the American Mathematical Society, Series B 9, no. 10 (March 29, 2022): 90–94. http://dx.doi.org/10.1090/bproc/69.

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We show that if γ \gamma is a curve in the unit disk, then arclength on γ \gamma is a Carleson measure iff the image of γ \gamma has finite length under every conformal map of the disk onto a bounded domain with a rectifiable boundary.
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29

Li, Songxiao, Junming Liu, and Cheng Yuan. "Embedding Theorems for Dirichlet Type Spaces." Canadian Mathematical Bulletin 63, no. 1 (July 22, 2019): 106–17. http://dx.doi.org/10.4153/s0008439519000201.

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AbstractWe use the Carleson measure-embedding theorem for weighted Bergman spaces to characterize the positive Borel measures $\unicode[STIX]{x1D707}$ on the unit disc such that certain analytic function spaces of Dirichlet type are embedded (compactly embedded) in certain tent spaces associated with a measure $\unicode[STIX]{x1D707}$. We apply these results to study Volterra operators and multipliers acting on the mentioned spaces of Dirichlet type.
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30

Lee, Ming-Yi. "Boundedness of Riesz transforms on weighted Carleson measure spaces." Studia Mathematica 209, no. 2 (2012): 169–87. http://dx.doi.org/10.4064/sm209-2-5.

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31

Lin, Chin-Cheng, and Kunchuan Wang. "Calderón–Zygmund operators acting on generalized Carleson measure spaces." Studia Mathematica 211, no. 3 (2012): 231–40. http://dx.doi.org/10.4064/sm211-3-4.

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32

Zhang, Yanhua. "Toeplitz Operator and Carleson Measure on Weighted Bloch Spaces." Journal of Function Spaces 2019 (February 17, 2019): 1–5. http://dx.doi.org/10.1155/2019/4358959.

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33

Haak, Bernhard H. "On the Carleson Measure Criterion in Linear Systems Theory." Complex Analysis and Operator Theory 4, no. 2 (February 24, 2009): 281–99. http://dx.doi.org/10.1007/s11785-009-0005-5.

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34

Jafari, F. "On Bounded and Compact Composition Operators in Polydiscs." Canadian Journal of Mathematics 42, no. 5 (October 1, 1990): 869–89. http://dx.doi.org/10.4153/cjm-1990-045-0.

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Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy and weighted Bergman spaces of the disc, and MacCluer [5] has made an extensive study of these opertors in the unit ball of Cn. Angular derivatives and Carleson measures have played an essential role in these studies. In this article we study composition operators in poly discs and characterize those operators which are bounded or compact in Hardy and weighted Bergman spaces. In addition to Carleson measure theorems resembling those of [5], [6], we give necessary and sufficient conditions satisfied by the maps inducing bounded or compact composition operators. We conclude by considering the role of angular derivatives on the compactness question explicitly.
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35

Zhou, Jizhen. "Predual ofQKSpaces." Journal of Function Spaces and Applications 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/252735.

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36

Qian, Ruishen, and Songxiao Li. "Carleson measure and Volterra type operators on weighted BMOA spaces." Georgian Mathematical Journal 27, no. 3 (September 1, 2020): 413–24. http://dx.doi.org/10.1515/gmj-2018-0040.

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AbstractLet μ be a nonnegative Borel measure on the unit disk {\mathbb{D}}. In this paper, we investigate measures μ such that the weighted {\mathrm{BMOA}} spaces are embedded boundedly or compactly into tent-type spaces {\mathcal{T}_{\varphi}^{\infty}(\mu)}. As an application, we characterize the boundedness and compactness of Volterra integral operators on the weighted {\mathrm{BMOA}} space.
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37

Gu, Dangsheng. "Two-Weight Norm Inequality and Carleson Measure in Weighted Hardy Spaces." Canadian Journal of Mathematics 44, no. 6 (October 1, 1992): 1206–19. http://dx.doi.org/10.4153/cjm-1992-072-9.

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AbstractLet (X, ν, d) be a homogeneous space and let Ω be a doubling measure on X. We study the characterization of measures μ on X+ = X x R+ such that the inequality , where q < p, holds for the maximal operator Hvf studied by Hörmander. The solution utilizes the concept of the “balayée” of the measure μ.
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38

Yang, Liu. "Integral operator acting on weighted Dirichlet spaces to Morrey type spaces." Filomat 33, no. 12 (2019): 3723–36. http://dx.doi.org/10.2298/fil1912723y.

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In this paper, we studied the boundedness and compactedness of integral operators from weighted Dirichlet spaces DK to Morrey type spaces H2K. Carleson measure and essential norm were also considered.
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39

Tan, Jian. "Weighted Hardy and Carleson measure spaces estimates for fractional integrations." Publicationes Mathematicae Debrecen 98, no. 3-4 (April 1, 2021): 313–30. http://dx.doi.org/10.5486/pmd.2021.8853.

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40

Pavicevic, Z. "The Carleson measure and meromorphic functions of uniformly bounded characteristic." Annales Academiae Scientiarum Fennicae Series A I Mathematica 16 (1991): 249–54. http://dx.doi.org/10.5186/aasfm.1991.1619.

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41

Hofmann, Steve, José María Martell, and Svitlana Mayboroda. "Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions." Duke Mathematical Journal 165, no. 12 (September 2016): 2331–89. http://dx.doi.org/10.1215/00127094-3477128.

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42

Kang, Hyeonbae, and Hyungwoon Koo. "Two-weighted inequalities for the derivatives of holomorphic functions and Carleson measures on the unit ball." Nagoya Mathematical Journal 158 (December 2000): 107–31. http://dx.doi.org/10.1017/s0027763000007340.

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AbstractWe characterize those positive measure µ’s on the higher dimensional unit ball such that “two-weighted inequalities” hold for holomorphic functions and their derivatives. Characterizations are given in terms of the Carleson measure conditions. The results of this paper also distinguish between the fractional and the tangential derivatives.
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43

Shamoyan, Romi. "On some characterizations of Carleson type measure in the unit ball." Banach Journal of Mathematical Analysis 3, no. 2 (2009): 42–48. http://dx.doi.org/10.15352/bjma/1261086707.

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44

Hofmann, Steve, Phi Le, and Andrew J. Morris. "Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations." Analysis & PDE 12, no. 8 (October 28, 2019): 2095–146. http://dx.doi.org/10.2140/apde.2019.12.2095.

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45

Tong, Cezhong, and Chen Yuan. "An integral operator preserving s-Carleson measure on the unit ball." Annales Academiae Scientiarum Fennicae Mathematica 40 (January 2015): 361–73. http://dx.doi.org/10.5186/aasfm.2015.4017.

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46

Freitas, Jorge Milhazes. "Continuity of SRB measure and entropy for Benedicks–Carleson quadratic maps." Nonlinearity 18, no. 2 (January 12, 2005): 831–54. http://dx.doi.org/10.1088/0951-7715/18/2/019.

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47

Charpentier, Stéphane, and Benoît Sehba. "Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces." Journal of Function Spaces and Applications 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/792763.

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We characterize those measuresμfor which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) spaceHΨ1(resp.,AαΨ1) of the unit ball ofCNembeds boundedly or compactly into the Orlicz spaceLΨ2(BN¯,μ)(resp.,LΨ2(BN,μ)), when the defining functionsΨ1andΨ2are growth functions such thatL1⊂LΨjforj∈{1,2}, and such thatΨ2/Ψ1is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators fromHΨ1(resp.,AαΨ1) intoHΨ2(resp.,AαΨ2).
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48

Zhai, Zhichun. "Carleson measure problems for parabolic Bergman spaces and homogeneous Sobolev spaces." Nonlinear Analysis: Theory, Methods & Applications 73, no. 8 (October 2010): 2611–30. http://dx.doi.org/10.1016/j.na.2010.06.040.

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49

Jie, Xiao. "Dual space, carleson measure and sequence interpolation onA p (ϕ)(O." Acta Mathematica Sinica 10, no. 2 (June 1994): 192–201. http://dx.doi.org/10.1007/bf02580426.

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50

Tan, Jian. "Some Hardy and Carleson measure spaces estimates for Bochner-Riesz means." Mathematical Inequalities & Applications, no. 3 (2020): 1027–39. http://dx.doi.org/10.7153/mia-2020-23-79.

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