ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

doi:10.1007/s10473-021-0114-4

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 241-256.doi: 10.1007/s10473-021-0114-4

ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

刘荣辉¹, 刘风², 伍火熊¹

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

收稿日期:2019-10-09 修回日期:2020-01-05 出版日期:2021-02-25 发布日期:2021-04-06
通讯作者: Huoxiong WU E-mail:huoxwu@xmu.edu.cn
作者简介:Ronghui LIU,E-mail:liuronghuimath@126.com;Feng LIU,E-mail:FLiu@sdust.edu.cn
基金资助:
The authors were partly supported by the NSFC (11771358, 11701333, 11871101).

ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

Ronghui LIU¹, Feng LIU², Huoxiong WU¹

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

Received:2019-10-09 Revised:2020-01-05 Online:2021-02-25 Published:2021-04-06
Contact: Huoxiong WU E-mail:huoxwu@xmu.edu.cn
About author:Ronghui LIU,E-mail:liuronghuimath@126.com;Feng LIU,E-mail:FLiu@sdust.edu.cn
Supported by:
The authors were partly supported by the NSFC (11771358, 11701333, 11871101).

摘要/Abstract

摘要： This paper studies the mixed radial-angular integrability of parametric Marcinki-ewicz integrals along "polynomial curves". Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.

关键词: Marcinkiewicz integrals, rough kernels, mixed radial-angular spaces

Abstract: This paper studies the mixed radial-angular integrability of parametric Marcinki-ewicz integrals along "polynomial curves". Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.

Key words: Marcinkiewicz integrals, rough kernels, mixed radial-angular spaces

中图分类号:

42B20

刘荣辉, 刘风, 伍火熊. ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS[J]. 数学物理学报(英文版), 2021, 41(1): 241-256.

Ronghui LIU, Feng LIU, Huoxiong WU. ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS[J]. Acta mathematica scientia,Series B, 2021, 41(1): 241-256.

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ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

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