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Journal articles on the topic 'Commutator estimates'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Taylor, Michael. "Commutator estimates." Proceedings of the American Mathematical Society 131, no. 5 (September 19, 2002): 1501–7. http://dx.doi.org/10.1090/s0002-9939-02-06723-0.

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2

Chen, Dongxiang, Dan Zou, and Suzhen Mao. "Multiple Weighted Estimates for Vector-Valued Multilinear Singular Integrals with Non-Smooth Kernels and Its Commutators." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/363916.

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This note concerns multiple weighted inequalities for vector-valued multilinear singular integral operator with nonsmooth kernel and its corresponding commutators containing multilinear commutator and iterated commutator generated by the vector-valued multilinear operator and BMO functions. By the weighted estimates for a class of new variant maximal and sharp maximal functions, the multiple weighted norm inequalities for such operators are obtained.
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3

Ber, A. F., and F. A. Sukochev. "Commutator estimates in $W^{*}$-factors." Transactions of the American Mathematical Society 364, no. 10 (October 1, 2012): 5571–87. http://dx.doi.org/10.1090/s0002-9947-2012-05568-1.

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4

Auscher, Pascal, and Michael E. Taylor. "Paradifferential operators and commutator estimates." Communications in Partial Differential Equations 20, no. 9-10 (January 1995): 1743–75. http://dx.doi.org/10.1080/03605309508821150.

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5

Ber, A. F., and F. A. Sukochev. "Commutator estimates in W⁎-algebras." Journal of Functional Analysis 262, no. 2 (January 2012): 537–68. http://dx.doi.org/10.1016/j.jfa.2011.09.018.

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6

Gao, Wen Hua. "Weighted BMO Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operator." Applied Mechanics and Materials 303-306 (February 2013): 1613–17. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1613.

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Schrödinger operator; Weighted BMO spaces; Reverse Hölder inequality; Commutator Abstract. In this paper, the Schrödinger operator on n dimensions Euclid space with the non-zero, nonnegative potential function satisfying the reverse Hölder inequality is considered. The weighted boundedness of the commutators composed of several Riesz transforms associated with the Schrödinger operator and weighted BMO function on weighted Lebesgue integral spaces are obtained, for some weighted function.
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7

Lai, Xudong. "Multilinear Estimates for Calderón Commutators." International Mathematics Research Notices 2020, no. 20 (August 31, 2018): 7097–138. http://dx.doi.org/10.1093/imrn/rny197.

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Abstract In this paper, we investigate the multilinear boundedness properties of the higher ($n$-th) order Calderón commutator for dimensions larger than two. We establish all multilinear endpoint estimates for the target space $L^{\frac{d}{d+n},\infty }(\mathbb{R}^d)$, including that Calderón commutator maps the product of Lorentz spaces $L^{d,1}(\mathbb{R}^d)\times \cdots \times L^{d,1}(\mathbb{R}^d)\times L^1(\mathbb{R}^d)$ to $L^{\frac{d}{d+n},\infty }(\mathbb{R}^d)$, which is the higher dimensional nontrivial generalization of the endpoint estimate that the $n$-th order Calderón commutator maps $L^{1}(\mathbb{R})\times \cdots \times L^{1}(\mathbb{R})\times L^1(\mathbb{R})$ to $L^{\frac{1}{1+n},\infty }(\mathbb{R})$. When considering the target space $L^{r}(\mathbb{R}^d)$ with $r<\frac{d}{d+n}$, some counterexamples are given to show that these multilinear estimates may not hold. The method in the present paper seems to have a wide range of applications and it can be applied to establish the similar results for Calderón commutator with a rough homogeneous kernel.
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8

Lenzmann, Enno, and Armin Schikorra. "Sharp commutator estimates via harmonic extensions." Nonlinear Analysis 193 (April 2020): 111375. http://dx.doi.org/10.1016/j.na.2018.10.017.

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9

Chen, Jiecheng, and Guoen Hu. "Weighted estimates for the Calderón commutator." Proceedings of the Edinburgh Mathematical Society 63, no. 1 (September 23, 2019): 169–92. http://dx.doi.org/10.1017/s001309151900021x.

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AbstractIn this paper the authors consider the weighted estimates for the Calderón commutator defined by \mathcal{C}_{m+1, A}(a_1,\ldots,a_{m};f)(x)={\rm p. v.} \displaystyle\int_{\mathbb{R}}\displaystyle\frac{P_2(A; x, y)\prod\nolimits_{j=1}^m(A_j(x)-A_j(y))}{(x-y)^{m+2}}f(y){\rm d}y,with P2(A;x, y) = A(x) − A(y) − A′(y)(x − y) and A′ ∈ BMO(ℝ). Dominating this operator by multi(sub)linear sparse operators, the authors establish the weighted bounds from $L^{p_1}(\mathbb {R},w_1) \times \cdots \times L^{p_{m+1}}(\mathbb {R},w_{m+1})$ to $L^{p}(\mathbb {R},\nu _{\vec {\kern 1pt w}})$, with p1, …, pm+1 ∈ (1, ∞), 1/p = 1/p1 + · · · + 1/pm+1, and $\vec {\kern 1pt w}=(w_1, \ldots , w_{m+1})\in A_{\vec {P}}(\mathbb {R}^{m+1})$. The authors also obtain the weighted weak type endpoint estimates for $\mathcal {C}_{m+1, A}$.
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10

Ber, A. F., and F. A. Sukochev. "Commutator estimates in von Neumann algebras." Functional Analysis and Its Applications 47, no. 1 (March 2013): 62–63. http://dx.doi.org/10.1007/s10688-013-0007-y.

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11

D’Ancona, Piero. "A Short Proof of Commutator Estimates." Journal of Fourier Analysis and Applications 25, no. 3 (April 24, 2018): 1134–46. http://dx.doi.org/10.1007/s00041-018-9612-8.

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12

LI, PENGTAO, and LIZHONG PENG. "ENDPOINT ESTIMATES FOR COMMUTATORS OF RIESZ TRANSFORMS ASSOCIATED WITH SCHRÖDINGER OPERATORS." Bulletin of the Australian Mathematical Society 82, no. 3 (August 16, 2010): 367–89. http://dx.doi.org/10.1017/s0004972710000390.

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AbstractIn this paper, we discuss the H1L-boundedness of commutators of Riesz transforms associated with the Schrödinger operator L=−△+V, where H1L(Rn) is the Hardy space associated with L. We assume that V (x) is a nonzero, nonnegative potential which belongs to Bq for some q>n/2. Let T1=V (x)(−△+V )−1, T2=V1/2(−△+V )−1/2 and T3 =∇(−△+V )−1/2. We prove that, for b∈BMO (Rn) , the commutator [b,T3 ] is not bounded from H1L(Rn) to L1 (Rn) as T3 itself. As an alternative, we obtain that [b,Ti ] , ( i=1,2,3 ) are of (H1L,L1weak) -boundedness.
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13

Dalmasso, Estefanía, Gladis Pradolini, and Wilfredo Ramos. "The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces." Fractional Calculus and Applied Analysis 21, no. 3 (June 26, 2018): 628–53. http://dx.doi.org/10.1515/fca-2018-0034.

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AbstractWe prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, includingLp-Lq,Lp-BMOandLp-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander’s type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values ofp.
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14

Gimperlein, Heiko, and Magnus Goffeng. "Commutator estimates on contact manifolds and applications." Journal of Noncommutative Geometry 13, no. 1 (March 11, 2019): 363–406. http://dx.doi.org/10.4171/jncg/326.

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15

Abdessemed, A., and E. B. Davies. "Some Commutator Estimates in the Schatten Classes." Journal of the London Mathematical Society s2-39, no. 2 (April 1989): 299–308. http://dx.doi.org/10.1112/jlms/s2-39.2.299.

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16

Hart, Jarod, and Virginia Naibo. "On Certain Commutator Estimates for Vector Fields." Journal of Geometric Analysis 28, no. 2 (May 4, 2017): 1202–32. http://dx.doi.org/10.1007/s12220-017-9859-3.

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17

Lai, Xudong. "Maximal Operator for the Higher Order Calderón Commutator." Canadian Journal of Mathematics 72, no. 5 (September 3, 2019): 1386–422. http://dx.doi.org/10.4153/s0008414x19000476.

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AbstractIn this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calderón commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the $L^{p}(\mathbb{R}^{d},w)$ space, including some peculiar endpoint estimates of the higher dimensional Calderón commutator.
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18

Liu, Lanzhe. "Sharp maximal function estimates and boundedness for commutators associated with general integral operator." Filomat 25, no. 4 (2011): 137–51. http://dx.doi.org/10.2298/fil1104137l.

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In this paper, we establish the sharp maximal function estimates for the commutator associated with some integral operator with general kernel and the weighted Lipschitz functions. As an application, we obtain the boundedness of the commutator on weighted Lebesgue, Morrey and Triebel-Lizorkin space. The operator includes Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.
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19

GOGATISHVILI, Amiran, Rza MUSTAFAYEV, and Müjdat AǦCAYAZI. "Weak-type Estimates in Morrey Spaces for Maximal Commutator and Commutator of Maximal Function." Tokyo Journal of Mathematics 41, no. 1 (June 2018): 193–218. http://dx.doi.org/10.3836/tjm/1502179258.

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20

Airta, Emil. "Two-weight commutator estimates: general multi-parameter framework." Publicacions Matemàtiques 64 (July 1, 2020): 681–729. http://dx.doi.org/10.5565/publmat6422013.

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21

Wu, Shuo, and Zhipei Niu. "Lipschitz estimates for the commutator of singular integral." Journal of Physics: Conference Series 1634 (September 2020): 012141. http://dx.doi.org/10.1088/1742-6596/1634/1/012141.

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22

Cerdà, Joan. "A note on commutator estimates for interpolation methods." Mathematische Nachrichten 280, no. 9-10 (July 2007): 1014–21. http://dx.doi.org/10.1002/mana.200510532.

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23

Hu, Guoen, and Wentan Yi. "Estimates for the commutator of bilinear Fourier multiplier." Czechoslovak Mathematical Journal 63, no. 4 (December 2013): 1113–34. http://dx.doi.org/10.1007/s10587-013-0074-5.

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24

Fan, Ming. "Commutator Estimates for Interpolation Scales with Holomorphic Structure." Complex Analysis and Operator Theory 4, no. 2 (April 4, 2009): 159–78. http://dx.doi.org/10.1007/s11785-009-0016-2.

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25

Wang, Zhiwei, and Lanzhe Liu. "Lipschitz Estimates for Multilinear Commutator of Pseudo-differential Operators." Annals of Functional Analysis 1, no. 2 (2010): 12–27. http://dx.doi.org/10.15352/afa/1399900584.

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26

Schikorra, Armin. "Three Examples of Sharp Commutator Estimates via Harmonic Extensions." Taiwanese Journal of Mathematics 23, no. 6 (December 2019): 1365–88. http://dx.doi.org/10.11650/tjm/190204.

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27

YANG, Jie, Yuzhao WANG, and Wenyi CHEN. "Endpoint estimates for the commutator of pseudo-differential operators." Acta Mathematica Scientia 34, no. 2 (March 2014): 387–93. http://dx.doi.org/10.1016/s0252-9602(14)60013-8.

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28

Hao, Jinliang, and Lanzhe Liu. "SHARP ESTIMATES FOR MULTILINEAR COMMUTATOR OF LITTLEWOOD-PALEY OPERATOR." Communications of the Korean Mathematical Society 23, no. 1 (January 31, 2008): 49–59. http://dx.doi.org/10.4134/ckms.2008.23.1.049.

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29

Kato, Tosio, and Gustavo Ponce. "Commutator estimates and the euler and navier-stokes equations." Communications on Pure and Applied Mathematics 41, no. 7 (October 1988): 891–907. http://dx.doi.org/10.1002/cpa.3160410704.

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30

Taylor, Michael E. "Commutator estimates for Hölder continuous and bmo-Sobolev multipliers." Proceedings of the American Mathematical Society 143, no. 12 (July 15, 2015): 5265–74. http://dx.doi.org/10.1090/proc/12825.

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31

Vakulenko, A. F. "On a variant of commutator estimates in spectral theory." Journal of Soviet Mathematics 49, no. 5 (May 1990): 1136–39. http://dx.doi.org/10.1007/bf02208709.

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32

Zhu, Xiaolin, and Lanzhe Liu. "Weighted Lipschitz Estimates for Multilinear Commutator of Multiplier Operator." Vietnam Journal of Mathematics 41, no. 3 (July 5, 2013): 255–67. http://dx.doi.org/10.1007/s10013-013-0018-2.

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33

Zhou, Xiaosha. "Lipschitz estimates for multilinear commutator of Littlewood-Paley operator." Rendiconti del Circolo Matematico di Palermo 58, no. 2 (July 18, 2009): 297–310. http://dx.doi.org/10.1007/s12215-009-0024-0.

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34

Fan, Ming. "Commutators in real interpolation with quasi-power parameters." Abstract and Applied Analysis 7, no. 5 (2002): 239–57. http://dx.doi.org/10.1155/s1085337502000830.

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The basic higher order commutator theorem is formulated for the real interpolation methods associated with the quasi-power parameters, that is, the function spaces on which Hardy inequalities are valid. This theorem unifies and extends various results given by Cwikel, Jawerth, Milman, Rochberg, and others, and incorporates some results of Kalton to the context of commutator estimates for the real interpolation methods.
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35

Wu, Changhong, and Meng Zhang. "Weighted endpoint estimates for multilinear commutator of Littlewood-Paley operator." Journal of Mathematical Inequalities, no. 3 (2011): 321–39. http://dx.doi.org/10.7153/jmi-05-29.

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36

de Pagter, Ben, and Fyodor Sukochev. "COMMUTATOR ESTIMATES AND $\RR$-FLOWS IN NON-COMMUTATIVE OPERATOR SPACES." Proceedings of the Edinburgh Mathematical Society 50, no. 2 (May 17, 2007): 293–324. http://dx.doi.org/10.1017/s0013091505000957.

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AbstractThe principal results in this paper are concerned with the description of domains of infinitesimal generators of strongly continuous groups of isometries in non-commutative operator spaces $E(\mathcal{M},\tau)$, which are induced by $\mathbb{R}$-flows on $\mathcal{M}$. In particular, we are concerned with the description of operator functions which leave the domain of such generators invariant in all symmetric operator spaces, associated with a semi-finite von Neumann algebra $\mathcal{M}$ and a separable function space $E$ on $(0,\infty)$. Furthermore, we apply our results to the study of operator functions for which $[D,x]\in E(\mathcal{M},\tau)$ implies that $[D,f(x)]\in E(\mathcal{M},\tau)$, where $D$ is an unbounded self-adjoint operator. Our methods are partly based on the recently developed theory of double operator integrals in symmetric operator spaces and the theory of adjoint $C_{0}$-semigroups.
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37

Caspers, Martijn, Fedor Sukochev, and Dmitriy Zanin. "Weak type operator Lipschitz and commutator estimates for commuting tuples." Annales de l’institut Fourier 68, no. 4 (2018): 1643–69. http://dx.doi.org/10.5802/aif.3195.

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38

Xu, Jiang. "A Young-like inequality with applications to the commutator estimates." Mathematical Inequalities & Applications, no. 2 (2015): 541–53. http://dx.doi.org/10.7153/mia-18-40.

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39

Jawerth, Björn, Richard Rochberg, and Guido Weiss. "Commutator and other second order estimates in real interpolation theory." Arkiv för Matematik 24, no. 1-2 (December 1985): 191–219. http://dx.doi.org/10.1007/bf02384398.

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40

Bouclet, Jean-Marc. "Low Frequency Estimates for Long Range Perturbations in Divergence Form." Canadian Journal of Mathematics 63, no. 5 (October 18, 2011): 961–91. http://dx.doi.org/10.4153/cjm-2011-022-9.

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Abstract We prove a uniformcontrol as z → 0 for the resolvent (P−z)−1 of long range perturbations P of the Euclidean Laplacian in divergence form by combining positive commutator estimates and properties of Riesz transforms. These estimates hold in dimension d ≥ 3 when P is defined on ℝd and in dimension d ≥ 2 when P is defined outside a compact obstacle with Dirichlet boundary conditions.
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41

Wang, Hua. "Two-Weight, Weak-Type Norm Inequalities for Fractional Integral Operators and Commutators on Weighted Morrey and Amalgam Spaces." Abstract and Applied Analysis 2020 (June 2, 2020): 1–23. http://dx.doi.org/10.1155/2020/3235942.

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Let 0<γ<n and Iγ be the fractional integral operator of order γ, Iγfx=∫ℝnx−yγ−nfydy and let b,Iγ be the linear commutator generated by a symbol function b and Iγ, b,Iγfx=bx⋅Iγfx−Iγbfx. This paper is concerned with two-weight, weak-type norm estimates for such operators on the weighted Morrey and amalgam spaces. Based on weak-type norm inequalities on weighted Lebesgue spaces and certain Ap-type conditions on pairs of weights, we can establish the weak-type norm inequalities for fractional integral operator Iγ as well as the corresponding commutator in the framework of weighted Morrey and amalgam spaces. Furthermore, some estimates for the extreme case are also obtained on these weighted spaces.
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42

Ding, Yong, and Shanzhen Lu. "Hardy spaces estimates for multilinear operators with homogeneous kernels." Nagoya Mathematical Journal 170 (2003): 117–33. http://dx.doi.org/10.1017/s0027763000008552.

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AbstractIn this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional integral operators with homogeneous kernels are bounded operators from the product spaces Lp1 × Lp2 × · · · × LpK (ℝn) to the Hardy spaces Hq (ℝn) and the weak Hardy space Hq,∞(ℝn), where the kernel functions Ωij satisfy only the Ls-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.
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43

Mancini, Gabriele, and Luca Martinazzi. "Extremals for Fractional Moser–Trudinger Inequalities in Dimension 1 via Harmonic Extensions and Commutator Estimates." Advanced Nonlinear Studies 20, no. 3 (August 1, 2020): 599–632. http://dx.doi.org/10.1515/ans-2020-2089.

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AbstractWe prove the existence of extremals for fractional Moser–Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the corresponding Euler–Lagrange equation, which requires new sharp estimates obtained via commutator techniques.
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44

Sarfraz, Naqash, Doaa Filali, Amjad Hussain, and Fahd Jarad. "Weighted Estimates for Commutator of Rough p -Adic Fractional Hardy Operator on Weighted p -Adic Herz–Morrey Spaces." Journal of Mathematics 2021 (May 28, 2021): 1–14. http://dx.doi.org/10.1155/2021/5559815.

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The current article investigates the boundedness criteria for the commutator of rough p -adic fractional Hardy operator on weighted p -adic Lebesgue and Herz-type spaces with the symbol function from weighted p -adic bounded mean oscillations and weighted p -adic Lipschitz spaces.
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45

Chen, X. L. Chen and D. X. "Two Weighted BMO Estimates for the Maximal Bochner-Riesz Commutator." Analysis in Theory and Applications 29, no. 2 (June 2013): 120–27. http://dx.doi.org/10.4208/ata.2013.v29.n2.3.

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46

Krugljak, Natan, and Mario Milman. "A distance between orbits that controls commutator estimates and invertibility of operators." Advances in Mathematics 182, no. 1 (February 2004): 78–123. http://dx.doi.org/10.1016/s0001-8708(03)00074-4.

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47

Caspers, M., D. Potapov, F. Sukochev, and D. Zanin. "Weak type commutator and Lipschitz estimates: resolution of the Nazarov-Peller conjecture." American Journal of Mathematics 141, no. 3 (2019): 593–610. http://dx.doi.org/10.1353/ajm.2019.0019.

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48

Cwikel, Michael, Nigel Kalton, Mario Milman, and Richard Rochberg. "A Unified Theory of Commutator Estimates for a Class of Interpolation Methods." Advances in Mathematics 169, no. 2 (August 2002): 241–312. http://dx.doi.org/10.1006/aima.2001.2061.

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49

Palsson, Eyvindur Ari. "Lp estimates for a singular integral operator motivated by Calderónʼs second commutator." Journal of Functional Analysis 262, no. 4 (February 2012): 1645–78. http://dx.doi.org/10.1016/j.jfa.2011.11.014.

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50

Gil’, Michael. "Estimates for Solutions of Differential Equations in a Banach Space via Commutators." Nonautonomous Dynamical Systems 5, no. 1 (February 28, 2018): 1–7. http://dx.doi.org/10.1515/msds-2018-0001.

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Abstract In a Banach space we consider the equation dx(t)/dt = (A + B(t))×(t) (t ≥ 0), where A is a constant bounded operator, and B(t) is a bounded variable operator.Norm estimates for the solutions of the considered equation are derived in terms of the commutator AB(t) − B(t)A. These estimates give us sharp stability conditions. Our results are new even in the finite dimensional case.We also discuss applications of the obtained results to a class of integro-differential equations.
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