Anisotropic singular integrals in product spaces

查看全文 作　　者：BOWNIK [1]Marcin

机构地区：[1]Department of Mathematics, University of Oregon

出　　处：《Science China Mathematics》索引2010年第53卷第12期,共16页

基　　金：supported by Start-up Funding Doctor of Xinjiang University(Grant No. BS090109);National Science Foundation of US (Grant No. DMS 0653881);National Natural Science Foundation of China (Grant No. 10871025) 摘　　要：In this paper, the authors introduce a class of product anisotropic singular integral operators, whose kernels are adapted to the action of a pair A := (A1, A2) of expansive dilations on R n and R m , respectively. This class is a generalization of product singular integrals with convolution kernels introduced in the isotropic setting by Fefferman and Stein. The authors establish the boundedness of these operators in weighted Lebesgue and Hardy spaces with weights in product A∞ Muckenhoupt weights on R n × R m . These results are new even in the unweighted setting for product anisotropic Hardy spaces. 关键词：expansive DILATION Muckenhoupt weight product SPACE HARDY SPACE BUMP function SINGULAR integral

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Anisotropic singular integrals in product spaces

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