Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1013-1022.

• • 下一篇

Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画

冀蕾¹(),魏明权^2,^*(),燕敦验¹()

¹中国科学院大学数学科学学院北京 100049
²信阳师范大学数学与统计学院河南信阳 464000

收稿日期:2023-10-17 修回日期:2025-01-03 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: *E-mail: weimingquan11@mails.ucas.ac.cn
作者简介:E-mail: jilei21@mails.ucas.ac.cn;|ydunyan@ucas.ac.cn
基金资助:
国家自然科学基金(12271501);国家自然科学基金(12301123);国家自然科学基金(12071052);信阳师范大学 "南湖学者奖励计划"青年项目

Characterizations of the Weak Boundedness for Commutators of Hardy-Type Operators on Central Morrey Spaces

Ji Lei¹(),Wei Mingquan^2,^*(),Yan Dunyan¹()

¹School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049
²School of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000

Received:2023-10-17 Revised:2025-01-03 Online:2025-08-26 Published:2025-08-01
Supported by:
NSFC(12271501);NSFC(12301123);NSFC(12071052);Nanhu Scholar Program for Young Scholars of Xinyang Normal University

摘要/Abstract

摘要：

该文给出了 $n$ 维 Hardy 型算子的交换子 $H_b$ 和 $H^*_b$ 从中心 Morrey 空间 $\dot{M}^{p,\lambda}(\mathbb{R}^n)$ 到弱中心 Morrey 空间 $W\dot{M}^{p,\lambda}(\mathbb{R}^n)$ 有界的一些刻画, 推广了 Lebesgue 空间上的相应结果.

关键词: $n$维 Hardy 型算子, 交换子, 弱中心 Morrey 空间, 弱中心有界平均振荡空间

Abstract:

We provide some characterizations of the boundedness for commutators of $n$-dimensional Hardy-type operators $H_b$ and $H^*_b$ from the central Morrey space $\dot{M}^{p,\lambda}(\mathbb{R}^n)$ to the weak central Morrey space $W\dot{M}^{p,\lambda}(\mathbb{R}^n)$, which extends the corresponding results on Lebesgue spaces.

Key words: $n$-dimensional Hardy-type operator, commutator, weak central Morrey space, weak central bounded mean oscillation space

中图分类号:

O174.2

冀蕾, 魏明权, 燕敦验. Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画[J]. 数学物理学报, 2025, 45(4): 1013-1022.

Ji Lei, Wei Mingquan, Yan Dunyan. Characterizations of the Weak Boundedness for Commutators of Hardy-Type Operators on Central Morrey Spaces[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1013-1022.

参考文献 29

[1]	Alvarez J, Lakey J, Guzmán-Partida M. Spaces of bounded $\lambda$-central mean oscilation, Morrey spaces,and $\lambda$-central Carleson measures. Collect Math, 2000, 51(3): 1-47
[2]	Bastero J, Milman M, Ruiz F J. Commutators of the maximal and sharp functions. Proc Amer Math Soc, 2000, 1.8: 3329-3334
[3]	Chanillo S. A note on commutators. Indiana Univ Math J, 1982, 31(1): 7-16
[4]	Christ M, Grafakos L. Best constants for two nonconvolution inequalities. Proc Amer Math Soc, 1995, 1.3(6): 1687-1693
[5]	Coifman R R, Rochberg R, Weiss G. Factorization theorems for Hardy spaces in several variables. Ann Math, 1976, 1.3: 611-635
[6]	Ding Y. A characterization of $\mathrm{BMO}$ via commutators for some operators. Northeast Math J, 1997, 13: 422-432
[7]	Ding Y, Lu S Z, Yabuta K. On commutators of Marcinkiewicz integrals with rough kernel. J Math Anal Appl, 2002, 2.5: 60-68
[8]	Faris W. Weak Lebesgue spaces and quantum mechanical binding. Duke Math J, 1976, 43: 365-373
[9]	Fu Z W, Liu Z G, Lu S Z, Wang H B. Characterization for commutators of $n$-dimensional fractional Hardy operators. Sci China Ser A, 2007, 50: 418-426
[10]	Fu Z W, Shi S G, Lu S Z. Two characterizations of central $\mathrm{BMO}$ space via the commutators of Hardy operators. Forum Math, 2021, 33(2): 505-529
[11]	Hardy G H, Littlewood J E, Pólya G. Inequalities. Cambrige: Cambridge University Press, 1952
[12]	He Q J, Wei M Q, Yan D Y. Characterizations of $p$-adic central Campanato spaces via commutator of $p$-adic Hardy type operators. J Korean Math Soc, 2019, 56(3): 767-787
[13]	John F, Nirenberg L. On functions of bounded mean oscillation. Comm Pure Appl Math, 1961, 2: 415-426
[14]	Komori Y. Notes on commutators of Hardy operators. Int J Pure Appl Math, 2003, 7: 329-334
[15]	Long S C, Wang J. Commutators of Hardy operators. J Math Anal Appl, 2002, 2.4: 626-644
[16]	Lu S Z, Fu Z W, Zhao F Y, Shi S G. Hardy Operators on Euclidean Spaces and Related Topics. Singapore: World Scientific, 2023
[17]	Meng Y, Yang D C. Boundedness of commutators with Lipschitz functions in nonhomogeneous spaces. Taiwanese J Math, 2006, 10: 1443-1464
[18]	Morrey C B. On the solutions of quasi-linear elliptic partial differential equations. Trans Amer Math Soc, 1938, 43(1): 126-166
[19]	Segovia C, Torrea J L. Vector-valued commutators and applications. Indiana Univ Math J, 1989, 38: 959-971
[20]	Shi S G, Fu Z W, Lu S Z. On the compactness of commutators of Hardy operators. Pacific J Math, 2020, 3.7(1): 239-256
[21]	Shi S G, Lu S Z. Characterization of the central Campanato space via the commutator operator of Hardy type. J Math Anal Appl, 2015, 4.9: 713-732
[22]	Tang C Q, Li Q G, Ma B L. Commutators of fractional integral operator associated to a nondoubling measures on metric spaces. Taiwanese J Math, 2009, 13: 1043-1052
[23]	Uchiyama A. On the compactness of operators of Hankel type. Tohoku Math J, 1978, 30(1): 163-171
[24]	王定怀, 周疆. 一类新型 $\mathrm{BMO}$ 空间. 数学学报, 2017, 60(5): 833-846 doi: 10.12386/A2017sxxb0071
	Wang D H, Zhou J. Some new classes of $\mathrm{BMO}$ spaces. Acta Mathematica Sinica, 2017, 60(5): 833-846 doi: 10.12386/A2017sxxb0071
[25]	Wang D H, Zhou J. Characterizations of the $\mathrm{BMO}$ and Lipschitz spaces via commutators on weak Lebesgue and Morrey spaces. Acta Math Appl, 2023, 39(3): 583-590
[26]	Wang D H, Zhou J, Chen W Y. Another characterization of Muckenhoupt $A_p$ class. Acta Math Sci, 2017, 37B(6): 1761-1774
[27]	Wei M Q. A characterization of $\mathrm{CBMO}^{\vec{q}}$ via the commutator of Hardy-type operators on mixed Herz spaces. Appl Anal, 2022, 1.1(16): 5727-5742
[28]	Wei M Q, Yan D Y. Sharp bounds for Hardy-type operators on mixed radial-angular central Morrey spaces. J Inequal Appl, 2023, 20.3(1): Article 31
[29]	Zhao F Y, Lu S Z. A characterization of $\lambda$-central $\mathrm{BMO}$ space. Front Math China, 2003, 8: 229-238

Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画

Characterizations of the Weak Boundedness for Commutators of Hardy-Type Operators on Central Morrey Spaces

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献 29

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	邵旭馗, 王素萍, 陶双平. 非齐次变指标 Herz-Morrey-Hardy 空间上的变量核 Marcinkiewicz 积分及其交换子[J]. 数学物理学报, 2025, 45(3): 653-664.
[2]	王瑶瑶, 吕玫钏, 李文明. 高维 Hardy 算子及其交换子的双权不等式[J]. 数学物理学报, 2024, 44(3): 539-546.
[3]	库福立. 多线性 Calderón-Zygmund 算子的交换子在广义 Morrey 空间上的紧性[J]. 数学物理学报, 2024, 44(2): 286-297.
[4]	程鑫, 张婧. 单边算子的多线性交换子在 Triebel-Lizorkin 空间上的加权有界性[J]. 数学物理学报, 2024, 44(1): 50-59.
[5]	杨雪纯,李宝德. 分数次极大奇异积分交换子的点态估计及其应用[J]. 数学物理学报, 2023, 43(4): 1024-1036.
[6]	徐宁,周泽华,丁颖. 单位球Hardy空间上加权复合算子的交换子[J]. 数学物理学报, 2021, 41(6): 1606-1615.
[7]	陈晓莉,陈冬香,朱红燕. 具有广义核的多线性平方算子与交换子的加权估计[J]. 数学物理学报, 2021, 41(4): 954-967.
[8]	邓宇龙,龙顺潮. ${A_{p}(\varphi)}$权, 拟微分算子及其交换子[J]. 数学物理学报, 2021, 41(2): 313-325.
[9]	逯光辉,陶双平. 度量测度空间上θ型Marcinkiewicz积分及交换子[J]. 数学物理学报, 2020, 40(6): 1431-1445.
[10]	陈冬香, 陈雪梅. 与Schrödinger算子相关的交换子的L^p-有界性[J]. 数学物理学报, 2016, 36(5): 832-847.
[11]	陈冬香, 周文娟, 房裕达. 与Schrödinger算子相关的Riesz位势算子的交换子的有界性[J]. 数学物理学报, 2016, 36(1): 117-129.
[12]	王松柏, 潘继斌, 江寅生. 多线性分数次积分算子有界的充分必要条件[J]. 数学物理学报, 2015, 35(6): 1106-1114.
[13]	郑庆玉, 张蕾, 石少广. 广义加权极大Morrey空间中次线性算子的有界性质[J]. 数学物理学报, 2015, 35(3): 503-514.
[14]	默会霞, 陆善镇. 带变量核的广义高阶Marcinkiewicz积分交换子在Herz型Hardy空间的有界性[J]. 数学物理学报, 2015, 35(1): 56-67.
[15]	王桦. Marcinkiewicz 算子的多线性交换子的Lipschitz估计[J]. 数学物理学报, 2014, 34(4): 977-991.