带变量核奇异积分算子的ρ-变差

数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1446-1460.

带变量核奇异积分算子的ρ-变差

龚珍兵(),陈艳萍*(),陶文宇()

北京科技大学数理学院北京 100083

收稿日期:2020-03-22 出版日期:2020-12-26 发布日期:2020-12-29
通讯作者: 陈艳萍 E-mail:gongzb@xs.ustb.edu.cn;yanpingch@126.com;wytao@xs.ustb.edu.cn
作者简介:龚珍兵, E-mail: gongzb@xs.ustb.edu.cn|陶文宇, E-mail:wytao@xs.ustb.edu.cn
基金资助:
国家自然科学基金(11871096);国家自然科学基金(11471033)

ρ-Variation for Singular Integral Operators with Variable Kernels

Zhenbing Gong(),Yanping Chen*(),Wenyu Tao()

Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083

Received:2020-03-22 Online:2020-12-26 Published:2020-12-29
Contact: Yanping Chen E-mail:gongzb@xs.ustb.edu.cn;yanpingch@126.com;wytao@xs.ustb.edu.cn
Supported by:
the NSFC(11871096);the NSFC(11471033)

摘要/Abstract

摘要：

该文证明了带粗糙变量核$\Omega\in L^{\infty}({\mathbb R}^{n})\times L^{q}({\mathbb S}^{n-1})$奇异积分算子的变差在$L^{2}({\mathbb R}^{n})$上的有界性, 其中$q>2(n-1)/n$, $n\geq2$.此外, 该文还得到了具有光滑变量核奇异积分算子的加权变差不等式并将其结果扩展到了Morrey空间.

关键词: 变差不等式, 变量核, 奇异积分, A_p权, Morrey空间

Abstract:

In this paper, we will prove that the variation of singular integral operators with rough variable kernels are bounded on $L^{2}({\mathbb S} ^{n})$ if $\Omega\in L^{\infty}({\mathbb R} ^{n})\times L^{q}({\mathbb S}^{n-1})$ for $q>2(n-1)/n$, and $n\geq2$. Moreover, we can also obtain the weighted variational inequalities for singular integral operators with smooth variable kernels. Finally, we extend the result to the Morrey spaces.

Key words: Variational inequalities, Variable kernel, Singular integral, A_p-weight, Morrey space

中图分类号:

O174.2

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.

Zhenbing Gong,Yanping Chen,Wenyu Tao. ρ-Variation for Singular Integral Operators with Variable Kernels[J]. Acta mathematica scientia,Series A, 2020, 40(6): 1446-1460.

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