Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/weighted-lp-documentclass-12pt-minimal-usepackage-amsmath-usepackage-rjZWksPasS
References (80)
-
B. Bongioanni, E. Harboure, O. Salinas (2011)
Classes of weights related to Schrödinger operatorsJournal of Mathematical Analysis and Applications, 373
-
Z Guo, P Li, L Peng (2008)
Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p}$$\end{document} boundedness of commutator of Riesz transform associated to Schrödinger operatorJ. Math. Anal. Appl., 341
-
T. Hytönen, S. Lappas (2020)
Extrapolation of compactness on weighted spaces: Bilinear operatorsIndagationes Mathematicae
-
Akihito Uchiyama (1978)
On the compactness of operators of Hankel typeTohoku Mathematical Journal, 30
-
Qingying Xue (2011)
Weighted estimates for the iterated commutators of multilinear maximal and fractional type operatorsStudia Mathematica, 217
-
ii) By a similar manner -
Yangyang Zhang, Long Huang, Dachun Yang, Wen Yuan (2022)
New Ball Campanato-Type Function Spaces and Their ApplicationsThe Journal of Geometric Analysis, 32
-
Example 2.19 (i) Let V ∈ B n . The operators ∇ L − 1 ∇ , ∇ -
Remark 1.1 (i) Theorems 3.2 and 3.5 can be applied to the Calderón–Zygmund operators related to Schrödinger type -
L. Tang, J. Wang, H. Zhu (2019)
Weighted Norm Inequalities for Area Functions Related to Schrödinger OperatorsJournal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 54
-
Á. Bényi, R. Torres (2013)
Compact Bilinear Operators and Commutators, 141
-
Dachun Yang, Dongyong Yang (2010)
Characterizations of localized BMO(ℝn) via commutators of localized Riesz transforms and fractional integrals associated to Schrödinger operatorsCollectanea mathematica, 61
-
Ryutaro, Eiichi (2019)
An extension of the characterization of CMO and its application to compact commutators on Morrey spaces -
Jin Tao, Qingying Xue, Dachun Yang, Wen Yuan (2019)
XMO and Weighted Compact Bilinear CommutatorsJournal of Fourier Analysis and Applications, 27
-
'Arp'ad B'enyi, Wendol'in Dami'an, Kabe Moen, R. Torres (2013)
Compact bilinear commutators: the weighted casearXiv: Classical Analysis and ODEs
-
Y Chen, Y Ding (2009)
Compactness of commutators of singular integrals with variable kernels (in Chinese)Chin. Ann. Math., 30
-
Jin Tao, Dachun Yang, D. Yang (2018)
Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spacesMathematical Methods in the Applied Sciences, 42
-
F. Beatrous, S. Li (1993)
On the Boundedness and Compactness of Operators of Hankel TypeJournal of Functional Analysis, 111
-
Hyunjoong Kim (2017)
Functional Analysis I -
Pengtao Li, T. Qian, Zhiyong Wang, Chao Zhang (2020)
Regularity of Fractional Heat Semigroup Associated with Schrödinger OperatorsFractal and Fractional
-
R. Torres, Qingying Xue (2020)
On compactness of commutators of multiplication and bilinear pseudodifferential operators and a new subspace of BMORevista Matematica Iberoamericana, 36
-
S. Janson, J. Peetre (1988)
Paracommutators—boundedness and Schatten-von Neumann propertiesTransactions of the American Mathematical Society, 305
-
K. Rothschild (2016)
A Course In Functional Analysis -
Y Ding, T Mei, Q Xue (2015)
Compactness of maximal commutators of bilinear Calderón–Zygmund singular integral operators. Some topics in Harmonic Analysis and applicationsAdv. Lect. Math., 34
-
D Yang, D Yang (2010)
Characterizations of localized BMO(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$BMO(\mathbb{R} ^{n})$$\end{document} via commutators of localized Riesz transforms and fractional integrals associated to Schrödinger operatorsCollect. Math., 61
-
T. Ma, P. Stinga, J. Torrea, Chao Zhang (2011)
Regularity estimates in Hölder spaces for Schrödinger operators via a $$T1$$ theoremAnnali di Matematica Pura ed Applicata, 193
-
Xianjie Yan, Dachun Yang, Wen Yuan (2020)
Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spacesFrontiers of Mathematics in China, 15
-
Yanping Chen, Yong Ding (2009)
Compactness characterization of commutators for Littlewood-Paley operatorsKodai Mathematical Journal, 32
-
Weichao Guo, Yongming Wen, Huo-xiong Wu, Dongyong Yang (2019)
On the compactness of oscillation and variation of commutatorsBanach Journal of Mathematical Analysis, 15
-
S Sugano (1998)
Estimates for the operators Vα(-Δ+V)-β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V^{\alpha }(-\Delta +V)^{-\beta }$$\end{document} and Vα∇(-Δ+V)-β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V^{\alpha }\nabla (-\Delta +V)^{-\beta }$$\end{document} with certain non-negative potentials V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V$$\end{document}Tokyo J. Math., 21
-
Rui Bu, Jiecheng Chen, G. Hu (2017)
Compactness for the commutator of Bochner-Riesz operatorActa Mathematica Scientia, 37
-
Á. Bényi, W. Damián, Kabe Moen, R. Torres (2013)
Compactness properties of commutators of bilinear fractional integralsMathematische Zeitschrift, 280
-
Shifen Wang, Qingying Xue (2021)
On weighted compactness of commutator of semi-group maximal function and fractional integrals associated to Schrödinger operatorsRevista Matemática Complutense, 35
-
A. Grigor’yan (2003)
Heat kernels and function theory on metric measure spaces -
B. Bongioanni, E. Harboure, Oscar Salinas (2011)
Weighted inequalities for commutators of Schrödinger–Riesz transformsJournal of Mathematical Analysis and Applications, 392
-
Lin Tang (2015)
Weighted norm inequalities for Schrödinger type operatorsForum Mathematicum, 27
-
A Uchiyama (1976)
On the compactness of operators of Hankel typeTôholu Math., 30
-
X Duong, J Li, S Mao, H Wu, D Yang (2018)
Compactness of Riesz transform commutator associated with Bessel operatorsJ. Anal. Math., 135
-
Jin Tao, Dachun Yang, D. Yang (2022)
A new vanishing Lipschitz-type subspace of BMO and compactness of bilinear commutatorsMathematische Annalen, 386
-
(1982)
HardySpacesonHomogeneousGroup -
L Liu, D Yang (2010)
Characterizations of BMO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$BMO$$\end{document} associated with Gauss measures via commutators of local fractional integralsIsr. J. Math., 180
-
Weichao Guo, Jianxun He, Huo-xiong Wu, Dongyong Yang (2018)
Boundedness and Compactness of Commutators Associated with Lipschitz FunctionsAnalysis and Applications
-
Yiqun Chen, H. Jia, Dachun Yang (2022)
Boundedness of Calderón–Zygmund operators on ball Campanato-type function spacesAnalysis and Mathematical Physics, 12
-
Zihua Guo, Pengtao Li, Lizhong Peng (2008)
Lp boundedness of commutators of Riesz transforms associated to Schrödinger operatorJournal of Mathematical Analysis and Applications, 341
-
iii) The weighted boundedness and compactness criteria obtained in the paper can also be applied to the cases of multilinear commutators which are defined by (2.5) -
Rui Bu, Jiecheng Chen (2014)
Compactness for the commutators of multilinear singular integral operators with non-smooth kernelsApplied Mathematics-A Journal of Chinese Universities, 34
-
Pengtao Li, Yan Mo, Chuangyuan Zhang (2015)
A compactness criterion and application to the commutators associated with Schrödinger operatorsMathematische Nachrichten, 288
-
Lucas Chaffee, Peng Chen, Yanchang Han, R. Torres, Lesley Ward (2017)
Characterization of compactness of commutators of bilinear singular integral operatorsProceedings of the American Mathematical Society
-
Pengtao Li, Lizhong Peng (2012)
Compact Commutators of Riesz Transforms Associated to Schrodinger OperatorPure and Applied Mathematics Quarterly, 8
-
P Li, L Peng (2012)
Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p}$$\end{document} boundeness of commutator operator associated with Schrödinger operators on Heisenberg groupActa Math. Sci., 32B
-
Weighted L p -boundedness and L p -compactness criteria -
S. Krantz, S. Li (2001)
Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, IIJournal of Mathematical Analysis and Applications, 258
-
L Peng (1988)
On the compactness of paracommutatorsArk. Math., 26
-
T. Hytonen, S. Lappas (2020)
Extrapolation of compactness on weighted spacesRevista Matemática Iberoamericana
-
Mingming Cao, Andrea Olivo, K. Yabuta (2020)
Extrapolation for multilinear compact operators and applicationsarXiv: Classical Analysis and ODEs
-
Semen Kutateladze (1996)
Fundamentals of Functional Analysis -
S. Krantz, S. Li (2001)
Regular ArticleBoundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, I☆Journal of Mathematical Analysis and Applications, 258
-
P. Lizhong (1988)
On the compactness of paracommutatorsArkiv för Matematik, 26
-
H. Cordes (1975)
On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operatorsJournal of Functional Analysis, 18
-
(1994)
On the Neumann problem for Schrödinger operators in Lipschitz domains -
Heping Liu, L. Tang (2009)
COMPACTNESS FOR HIGHER ORDER COMMUTATORS OF OSCILLATORY SINGULAR INTEGRAL OPERATORSInternational Journal of Mathematics, 20
-
Xing Fu, Dachun Yang, Sibei Yang (2020)
Endpoint Boundedness of Linear Commutators on Local Hardy Spaces Over Metric Measure Spaces of Homogeneous TypeThe Journal of Geometric Analysis, 31
-
Shifen Wang, Qingying Xue (2020)
On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operatorsForum Mathematicum, 34
-
Qingying Xue, K. Yabuta, Jingquan Yan (2018)
Weighted Fréchet–Kolmogorov Theorem and Compactness of Vector-Valued Multilinear OperatorsThe Journal of Geometric Analysis, 31
-
Satoko Sugano (1998)
Estimates for the Operators $V^{\alpha}(-\Delta+V)^{-\beta}$ and $V^{\alpha}\nabla(-\Delta+V)^{-\beta}$ with Certain Non-negative Potentials $V$Tokyo Journal of Mathematics, 21
-
Jin Tao, Dachun Yang, Wen Yuan, Yangyang Zhang (2021)
Compactness Characterizations of Commutators on Ball Banach Function SpacesPotential Analysis, 58
-
B. Bongioanni, E. Harboure, Oscar Salinas (2011)
Commutators of Riesz Transforms Related to Schrödinger OperatorsJournal of Fourier Analysis and Applications, 17
-
Zhongwei Shen (1995)
$L^p$ estimates for Schrödinger operators with certain potentialsAnnales de l'Institut Fourier, 45
-
Liguang Liu, Dachun Yang (2009)
Characterizations of BMO associated with Gauss measures via commutators of local fractional integralsIsrael Journal of Mathematics, 180
-
Lucas Chaffee, R. Torres (2014)
Characterization of Compactness of the Commutators of Bilinear Fractional Integral OperatorsPotential Analysis, 43
-
Ryutaro Arai, E. Nakai (2020)
An extension of the characterization of $\mathrm{CMO}$ and its application to compact commutators on Morrey spacesJournal of The Mathematical Society of Japan, 72
-
L. Pengtao, P. Lizhong (2012)
Lp boundedness of commutator operator associated with schrödinger operators on heisenberg groupActa Mathematica Scientia, 32
-
Chin-Cheng Lin, Heping Liu, Yu Liu (2011)
Hardy spaces associated with Schrodinger operators on the Heisenberg grouparXiv: Analysis of PDEs
-
Qianjun He, Pengtao Li (2022)
On Weighted Compactness of Commutators Related with Schrödinger OperatorsActa Mathematica Sinica, English Series, 38
-
Remark 1.2 (i) The weight class A ρ,θ p considered in this paper is a generalization of the class of A p weights -
X. Duong, Ji Li, Suzhen Mao, Huo-xiong Wu, Dongyong Yang (2016)
Compactness of Riesz transform commutator associated with Bessel operatorsJournal d'Analyse Mathématique, 135
-
T. Hytonen, S. Lappas (2020)
Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates.arXiv: Functional Analysis
-
Xiao-mei Wu, Xiao Yu (2019)
Compactness of the commutators of intrinsic square functions on weighted Lebesgue spacesTURKISH JOURNAL OF MATHEMATICS
-
Jin Tao, Dachun Yang, D. Yang (2019)
Beurling–Ahlfors Commutators on Weighted Morrey Spaces and Applications to Beltrami EquationsPotential Analysis, 53
-
Yanping Chen, Yong Ding, Xinxia Wang (2011)
Compactness for Commutators of Marcinkiewicz Integrals in Morrey SpacesTaiwanese Journal of Mathematics, 15
- Publisher
- Springer Journals
- Copyright
- Copyright © Tusi Mathematical Research Group (TMRG) 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
- ISSN
- 2662-2033
- eISSN
- 1735-8787
- DOI
- 10.1007/s43037-023-00273-2
- Publisher site
- See Article on Publisher Site
Abstract
Let T be a bounded operator on Lp(Rn)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{p}({\mathbb {R}}^{n})$$\end{document} and Ap/m′ρ,θ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ A_{p/m'}^{\rho ,\theta }$$\end{document} denote the class of Ap\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A_{p}$$\end{document} type weights related with Schrödinger operators L=-Δ+V\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L=-\Delta +V$$\end{document}, where V belongs to the reverse Hölder class Bq\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_{q}$$\end{document}. In this paper, under the assumption that the kernel of T satisfies some Hörmander type estimates, we obtain a boundedness criterion for the commutators [b, T] on the weighted Lebesgue spaces Lp(ω)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{p}(\omega )$$\end{document} with b∈BMOθ(ρ)(Rn)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$b\in \textrm{BMO}_{\theta }(\rho )({\mathbb {R}}^{n})$$\end{document} and ω∈Ap/m′ρ,θ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\omega \in A_{p/m'}^{\rho ,\theta }$$\end{document}, where BMOθ(ρ)(Rn)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\textrm{BMO}_{\theta }(\rho )(\mathbb R^{n})$$\end{document} denotes the BMO type spaces related with L. Further, for b∈CMOθ(ρ)(Rn)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$b\in \textrm{CMO}_{\theta }(\rho )({\mathbb {R}}^{n})$$\end{document}, the vanishing BMO type space related with L, a criterion of Lp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{p}$$\end{document}-weighted compactness of [b, T], is established.
Journal
Banach Journal of Mathematical Analysis – Springer Journals
Published: Jul 1, 2023
Keywords: Compactness; Boundedness; Weight functions; Commutators; 22E30; 42B35; 35J10; 47B38