混合勒贝格空间上双参数奇异积分算子的端点弱估计  

ENDPOINT WEAK-TYPE ESTIMATES OF BI-PARAMETER SINGULAR INTEGRAL OPERATORS ON MIXED LEBESGUE SPACES

作　　者：王潇 WANG Xiao(School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China)

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《数学杂志》2023年第3期202-212,共11页Journal of Mathematics

摘　　要：本文研究了混合勒贝格空间上双参数奇异积分算子的有界性.利用双参数奇异积分算子在勒贝格空间的有界性和一个向量值延拓理论.获得了双参数奇异积分算子在混合勒贝格空间上的端点弱估计和强型估计.并给出了乘积空间上非卷积型奇异积分算子的一个应用.这些结果将文献[3]中的结论推广到混合范数情形.In this paper,the boundedness of the bi-parameter singular integral operators on mixed Lebesgue spaces is studied.Using the boundedness of the bi-parameter singular integral operators on Lebesgue spaces and a vector-valued extension theory.We obtain the endpoint weak-type estimates and strong-type estimates for a bi-parameter singular integral operators on mixed Lebesgue spaces.An application to a non-convolution singular integral operators on product spaces is also given.These results extend the conclusion of[3]to the mixed norm case.

关 键 词：双参数奇异积分算子 混合范数 端点弱估计 

分 类 号：O174.2[理学—数学]