多线性 Calderón-Zygmund 算子的交换子在广义 Morrey 空间上的紧性

多线性 Calderón-Zygmund 算子的交换子在广义 Morrey 空间上的紧性

Compact Commutators of $m$ -Linear Calderón-Zygmund Operators on Generalized Morrey Spaces

摘要/Abstract

参考文献 28

相关文章 15

Metrics

数学物理学报 ›› 2024, Vol. 44 ›› Issue (2): 286-297.

库福立()

三明学院信息工程学院福建三明 365004

收稿日期:2022-12-14 修回日期:2023-09-27 出版日期:2024-04-26 发布日期:2024-04-07
作者简介:库福立,Email:kfl20180325@163.com
基金资助:
国家自然科学基金(12171399);国家自然科学基金(11871101);三明学院引进高层次人才科研启动经费(23YG09);福建省教育厅重点项目(JZ230054)

Ku Fuli()

School of Information Engineering, Sanming University, Fujian Sanming 365004

Received:2022-12-14 Revised:2023-09-27 Online:2024-04-26 Published:2024-04-07
Supported by:
NSFC(12171399);NSFC(11871101);Scientific Research Start-up Fund Project for Introducing High-Ievel Talents From Sanming University(23YG09);Key project of Fujian Provincial Education Department(JZ230054)

摘要：

该文研究了多线性 $\omega$ 型 Calderón-Zygmund 算子与带变量增长条件的广义 Campanato 空间函数 $\vec{b}$ 生成的交换子 $[\vec{b},T]$ 在广义 Morrey 空间的紧性, 给出了 $[\vec{b},T]$ 是从广义 Morrey 空间的乘积空间到广义 Morrey 空间的紧算子的充分条件.

关键词: 多线性 Calderón-Zygmund 算子, 交换子, Campanato 空间, 广义 Morrey 空间, 紧性

Abstract:

In this paper, the compactness of commutator $[\vec{b},T]$ generated by the $m$ -linear $\omega$ -type C-Z operator and generalized Campanato space function $\vec{b}$ with variable growth conditions on generalized Morrey space is studied. A sufficient condition for the compactness of commutator $[\vec{b},T ]$ is obtained on the generalized Morrey space.

Key words: Multilinear Calderón-Zygmund operator, Commutator, Campanato spaces, Generalized Morrey spaces, Compactness

中图分类号:

O174.2

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.

Ku Fuli. Compact Commutators of $m$ -Linear Calderón-Zygmund Operators on Generalized Morrey Spaces[J]. Acta mathematica scientia,Series A, 2024, 44(2): 286-297.

[1]	Calderón A P, Zygmund A. On the existence of certain singular integrals. Acta Math, 1952, 88: 85-139
[2]	Yabuta K. Generalizations of Calderón-Zygmund operators. Studia Math, 1985, 82(1): 17-31 doi: 10.4064/sm-82-1-17-31
[3]	Maldonado D, Naibo V. Weighted norm inequalities for paraproducts and bilinear pseudodifferential operators with mild regularity. J Fourier Anal Appl, 2009, 15(2): 218-261 doi: 10.1007/s00041-008-9029-x
[4]	Lu G Z, Zhang P. Multilinear Calderón-Zygmund operators with kernels of Dini's type and applications. Nonlinear Anal, 2014, 107: 92-117
[5]	Arai R, Nakai E. Commutators of Calderón-Zygmund and generalized fractional integral operators on generalized Morrey spaces. Rev Mat Complut, 2018, 31(2): 287-331 doi: 10.1007/s13163-017-0251-4
[6]	Ku F L. Boundedness of commutators for multilinear Calderón-Zygmund operators on generalized Morrey spaces. arXiv.2312.08941
[7]	Lerner A, Ombrosi S, Pérez C, et al. New maximal functions and multiple weights for the multi-linear Calderón-Zygmund theory. Adv Math, 2009, 220(4): 1222-1264 doi: 10.1016/j.aim.2008.10.014
[8]	Uchiyama A. On the compactness of operators of Hankel type. Tôhoku Math J, 1978, 30(1): 163-171
[9]	Coifman R R, Lions P L, Meyer Y, Semmes S. Compensated compactness and Hardy spaces. J Math Pures Appl, 1993, 72(3): 247-286
[10]	Betancor J J, Fari $\tilde{\rm n}$ a J C. A note on compactness of commutators for fractional integrals associated with nondoubling measures. Z Anal Anwend, 2007, 26(3): 331-339 doi: 10.4171/zaa
[11]	Chen Y P, Ding Y, Wang X X. Compactness of commutators for singular integrals on Morrey spaces. Canad J Math, 2012, 64(2): 257-281 doi: 10.4153/CJM-2011-043-1
[12]	Ding Y, Mei T. Boundedness and compactness for the commutators of bilinear operators on Morrey spaces. Potential Anal, 2015, 42(3): 717-748 doi: 10.1007/s11118-014-9455-0
[13]	Torres R H, Xue Q Y, Yan Q J. Compact bilinear commutators: the quasi-Banach space case. J Anal, 2018, 26(2): 227-234
[14]	Arai R, Nakai E. Compact commutators of Calderón-Zygmund and generalized fractional integral operators with a function in generalized Campanato spaces on generalized Morrey spaces. Tokyo J Math, 2019, 42(2): 471-496
[15]	Gafakos L, Torres R H. Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ Math J, 2002, 51(5): 1261-1276 doi: 10.1512/iumj.2002.51.2114
[16]	Rao M M, Ren Z D. Theory of Orlicz Spaces. New York: Marcel Dekker, 1991
[17]	Bényi Á, Torres R H. Compact bilinear operators and commutators. Proc Amer Math Soc, 2013, 141(10): 3609-3621 doi: 10.1090/proc/2013-141-10
[18]	Bényi Á, Damián W, Moen K, Torres R H. Compactness properties of commutators of bilinear fractional integrals. Math Z, 2015, 280(1/2): 569-582 doi: 10.1007/s00209-015-1437-4
[19]	Cruz-Uribe D, Martell J M, Pérez C. Sharp weighted estimates for classical operators. Adv Math, 2012, 229(1): 408-441 doi: 10.1016/j.aim.2011.08.013
[20]	Coifman R R, Meyer Y. On commutators of singular integrals and bilinear singular integrals. Trans Amer Math Soc, 1975, 212: 315-331
[21]	Coifman R R, Meyer Y. Commutateurs d'intégrales singulières et opérateurs multilinéaires. Ann Inst Fourier (Grenoble), 1978, 28 (3): 177-202 doi: 10.5802/aif.708
[22]	Chanillo S. A note on commutators. Indiana Univ Math J, 1982, 31(1): 7-16 doi: 10.1512/iumj.1982.31.31002
[23]	Chen S Q, Wu H X. Multiple weighted estimates for commutators of multilinear singular integrals with non-smooth kernels. J Math Anal Appl, 2012, 396(2): 888-903 doi: 10.1016/j.jmaa.2012.07.038
[24]	Chen X, Xue Q Y, Yabuta K. On multilinear Littlewood-Paley operators. Nonlinear Anal, 2015, 115: 25-40
[25]	Fazio G Di, Ragusa M A. Commutators and Morrey spaces. Boll Un Mat Ital A, 1991, 5(3): 323-332
[26]	Kenig C E, Stein E M. Multilinear estimates and fractional integration. Math Res Lett, 1999, 6(1): 1-15 doi: 10.4310/MRL.1999.v6.n1.a1
[27]	Wang P W, Liu Z G. Boundedness of multilinear integral operators and their commutators on generalized Morrey spaces. Adv Oper Theory, 2017, 2(3): 269-286
[28]	Grafakos L, Torres R H. Multilinear Calderón-Zygmund theory. Adv Math, 2002, 165(1): 124-164 doi: 10.1006/aima.2001.2028

[1]	刘鑫艳, 李晓光. 一类非齐次非线性 Schrödinger 方程驻波的轨道稳定性[J]. 数学物理学报, 2024, 44(2): 476-483.
[2]	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.
[3]	沈钦锐,孙俊俊. Hilbert空间中的算子非紧性测度[J]. 数学物理学报, 2023, 43(4): 1003-1008.
[4]	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.
[5]	李易娴,张正杰. 一类与 Klein-Gordon-Maxwell 问题有关的方程组的基态解的存在性[J]. 数学物理学报, 2023, 43(3): 680-690.
[6]	李永祥,韦启林. Banach空间半线性发展方程周期解的存在性结果及应用[J]. 数学物理学报, 2023, 43(3): 702-712.
[7]	李扬荣, 王凤玲, 杨爽. 带非线性噪音的随机 ${g}$ -Navier-Stokes方程的后向弱紧均值动力学[J]. 数学物理学报, 2023, 43(2): 531-548.
[8]	陈洪欣,张学军,周敏. $\boldsymbol{H^{p,q,s}}({\Bbb D})$ 上的复合算子[J]. 数学物理学报, 2023, 43(1): 1-13.
[9]	李安然,樊丹丹,魏重庆. 临界零质量Kirchhoff型方程的解及其渐近行为[J]. 数学物理学报, 2022, 42(6): 1729-1743.
[10]	刘文杰,谢胜利. 脉冲无穷时滞中立型测度微分方程mild解的存在性[J]. 数学物理学报, 2022, 42(6): 1671-1681.
[11]	郭雨婷,张学军. 正规权一般函数空间到Bloch型空间的复合算子[J]. 数学物理学报, 2022, 42(5): 1306-1319.
[12]	许文丁,钟婷. 非光滑牛顿算法的收敛性[J]. 数学物理学报, 2022, 42(5): 1537-1550.
[13]	何泽荣,周楠. 具有年龄等级结构的种群竞争系统的最优收获控制[J]. 数学物理学报, 2022, 42(1): 228-244.
[14]	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.
[15]	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.

Just accepted

Online first

Just accepted

Online first

Viewed

Full text

	From	local

	Times	71
	Rate	100%

Abstract

Just accepted	Online first	Issue

0	0	71

From	Others	local

Times	70	1
Rate	99%	1%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed