非齐次变指标 Herz-Morrey-Hardy 空间上的变量核 Marcinkiewicz 积分及其交换子

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 653-664.

• • 下一篇

非齐次变指标 Herz-Morrey-Hardy 空间上的变量核 Marcinkiewicz 积分及其交换子

邵旭馗^1,^*,王素萍¹(),陶双平²

¹陇东学院数学与信息工程学院甘肃庆阳 745000
²西北师范大学数学与统计学院兰州 730070

收稿日期:2024-09-26 修回日期:2025-01-20 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *邵旭馗
作者简介:王素萍,E-mail: shwangsp@126.com
基金资助:
国家自然科学基金(12361018);甘肃省自然科学基金(23JRRM730);甘肃省自然科学基金(22JR11RM165);庆阳市联合科研基金(QY-STK-2024A-069);陇东学院博士基金(XYBYZK2112);陇东学院博士基金(XYBYZK2113)

Variable Kernel Marcinkiewicz Integral and its Commutator on the Nonhomogeneous Variable Exponent Herz-Morrey-Hardy Space

Shao Xukui^1,^*,Wang Suping¹(),Tao Shuangping²

¹School of Mathematics and Information Engineering, Longdong University, Gansu Qingyang 745000
²School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070

Received:2024-09-26 Revised:2025-01-20 Online:2025-06-26 Published:2025-06-20
Supported by:
NSFC(12361018);Natural Science Foundation of Gansu Province(23JRRM730);Natural Science Foundation of Gansu Province(22JR11RM165);Joint Research Foundation of Qingyang(QY-STK-2024A-069);Longdong University Doctor Foundation(XYBYZK2112);Longdong University Doctor Foundation(XYBYZK2113)

摘要/Abstract

摘要：

应用核函数 $\Omega(x,z)$ 的性质, 讨论了变量核参数型 Marcinkiewicz 积分算子 $\mu^{\theta}_{\Omega}$ 及其与 $\mathrm{BMO}(\mathbb{R}^{n})$ 函数 $b$ 生成的交换子 $\mu^{\theta}_{\Omega,b}$ 在非齐次变指标 Herz-Morrey-Hardy 空间上的有界性, 从而推广了以往的研究结果.

关键词: Marcinkiewicz 积分, 交换子, 变量核, 非齐次变指标 Herz-Morrey-Hardy 空间

Abstract:

By the property about the function $\Omega(x,z)$, the boundedness of parameterized Marcinkiewicz integral operators with variable kernels $\mu^{\theta}_{\Omega}$ and their commutator $\mu^{\theta}_{\Omega,b}$ generated by $ \mathrm{BMO}(\mathbb{R}^{n})$ functions $b$ are established on the nonhomogeneous variable exponent Herz-Morrey-Hardy space, which extends results that have been achieved in previous research.

Key words: Marcinkiewicz integral, commutators, variable kernel, nonhomogeneous variable exponent Herz-Morrey-Hardy space

中图分类号:

O174.2

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.

Shao Xukui, Wang Suping, Tao Shuangping. Variable Kernel Marcinkiewicz Integral and its Commutator on the Nonhomogeneous Variable Exponent Herz-Morrey-Hardy Space[J]. Acta mathematica scientia,Series A, 2025, 45(3): 653-664.

参考文献

[1]	Ding Y, Lin Q C, Shao S L. On Marcinkiewicz integral with variable kernels. Indiana Univ Math J, 2004, 53: 805-821
[2]	Xue Q Y, Yabuta K. $L^{2}$-Boundedness of Marcinkiewicz integrals along surfaces with variable kernels. Sci Math Jpn, 2006, 63(3): 369-382
[3]	陶双平, 邵旭馗. 带变量核的 Marcinkiewicz 积分算子在齐次 Morrey-Herz 空间的有界性. 兰州大学学报 (自然科学版), 2010, 46(3): 102-107
[3]	Tao S P, Shao X K. Boundedness of Marcinkiewicz integrals with variable kernel on the homogeneous Morrey-Herz spaces. Journal of Lanzhou University (Natural Science), 2010, 46(3): 102-107
[4]	陶祥兴, 位瑞英. 可变核 Marcinkiewicz 积分交换子在 Herz 型 Hardy 空间上的有界性. 数学物理学报, 2009, 29A(6): 1508-1517
[4]	Tao X X, Wei R Y. Boundedness of commutators related to Marcinkiewicz integrals with variable kernels in Herz-type Hardy spaces. Acta Math Sci, 2009, 29A(6): 1508-1517
[5]	王洪彬, 傅尊伟, 刘宗光. 变指标 Lebesgue 空间上的 Marcinkiewicz 积分高阶交换子. 数学物理学报, 2012, 32A(6): 1092-1101
[5]	Fu Z W, Liu Z G. Higher-order commutators of Marcinkiewicz integrals on variable Lebesgue spaces. Acta Math Sci, 2012, 32A(6): 1092-1101
[6]	邵旭馗, 陶双平. 变量核 Marcinkiewicz 积分及其交换子在变指标 Morrey 空间上的有界性. 数学物理学报, 2018, 38A(6): 1067-1075
[6]	Tao S P. Boundedness of Marcinkiewicz integrals and commutators with variable kernel on Morrey spaces with variable exponents. Acta Math Sci, 2018, 38A(6): 1067-1075
[7]	Han Y Y, Wu H X. The Fractional type Marcinkiewicz integrals and commutators on weighted Hardy spaces. Acta Math Sci, 2023, 43B(5): 1981-1996
[8]	Wang H, Zhang C J. A note on parameterized Marcinkiewicz integrals with variable kernels. Appl Math J Chinese Univ Ser B, 2009, 24(3): 315-320
[9]	Chen Y P, Ding Y. Boundedness of commutators of Marcinkiewicz integral with rough variable kernel. Integral Equations and Operator Theory, 2008, 61: 477-492
[10]	Mo H X, Lu S Z. Generalized commutators for Marcinkiewicz type integrals with variable kernels. Acta Math Appl Sin Engl Ser, 2011, 27(3): 471-480
[11]	Orlicz W. Uber konjugierte Exponentenfolgen. Studia Math, 1931, 3: 200-211
[12]	Ruzika M. Electrorheological Fluids:Modeling and Mathematical Theory. Berlin: Springer, 2000, 1748: 16-38
[13]	Harjulehto P, H?st? P, Latvala V, Toivanen O. Critical variable exponent functionals in image restoration. Appl Math Lett, 2013, 26(1): 56-60
[14]	Zhikov V. Averaging of functionals of the calculus of variations and elasticity theory. Math USSR Izv, 1987 29: 33-66
[15]	Ková?ik O, Rákosník J. On spaces $L^{p(x)}$ and $W^{k,p(x)}$. Czechoslovak Math J, 1991, 41(4): 592-618
[16]	Nakano K. Modulared Semi-Ordered Linear Spaces. Tokyo: Maruzen Co Ltd, 1950
[17]	Nakano K. Topology of Linear Topological Spaces. Tokyo: Maruzen Co Ltd, 1951
[18]	Izuki M. Boundedness of vector-valued sublinear operators on Herz-Morrey spaces with variable exponent. Math Sci Res J, 2009, 13: 243-253
[19]	Izuki M. Fractional integrals on Herz-Morrey spaces with variable exponent. Hiroshima Math J, 2010, 40: 343-355
[20]	Wang H B, Liu Z G. The Herz-type Hardy spaces with variable exponent and their applications. Taiwanese J Math, 2012, 16(4): 1363-1389
[21]	Xu J S, Yang X D. Herz-Morrey-Hardy spaces with variable exponents and their applications. Journal of Function Spaces, 2015, 2015(318): 1-19
[22]	Shao X K, Tao S P. Weighted estimates of variable kernel fractional integral and its commutators on vanishing generalized Morrey spaces with variable exponent. Chin Ann Math Ser B, 2021, 42(3): 451-470
[23]	邵旭馗, 陶双平. 变指标弱 Herz 空间上的变量核分数次积分算子. 应用数学, 2023, 36(1): 213-219
[23]	Tao S P. Fractional integral operators with variable kernels on variable exponent weak Herz spaces. Math Appl, 2023, 36(1): 213-219
[24]	Wang H B, Liu Z G. Boundedness of singular integral operators on weak Herz spaces with variable exponent. Ann Funct Anal, 2020, 11: 1108-1125
[25]	Lu S Z, Yang D, Hu G E. Herz Type Spaces and Their Applications. Beijing: Science Press, 2008
[26]	Karlovich A Y, Lerner A K. Commutators of singular integrals on generalized $L^p$ spaces with variable exponent. Publ Mat, 2005, 49: 111-125
[27]	Wang H. Boundedness of several integral operators with bounded variable kernels on Hardy and weak Hardy spaces. Internat J Math, 2013, 24: 1-22

非齐次变指标 Herz-Morrey-Hardy 空间上的变量核 Marcinkiewicz 积分及其交换子

Variable Kernel Marcinkiewicz Integral and its Commutator on the Nonhomogeneous Variable Exponent Herz-Morrey-Hardy Space

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	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.
[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]	龚珍兵,陈艳萍,陶文宇. 带变量核奇异积分算子的ρ-变差[J]. 数学物理学报, 2020, 40(6): 1446-1460.
[11]	邵旭馗,陶双平. 变量核Marcinkiewicz积分及其交换子在变指标Morrey空间上的有界性[J]. 数学物理学报, 2018, 38(6): 1067-1075.
[12]	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.
[13]	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.
[14]	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.
[15]	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.