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.

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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

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