ROUGH SINGULAR INTEGRALS SUPPORTED BY SUBMANIFOLDS IN TRIEBEL-LIZORKIN SPACES AND BESOVE SPACES

This paper is devoted to studying the singular integral operators associated to polynomial mappings as well as the corresponding compound submanifolds. By imposing a restrictive condition on the kernels of the operators in the radial direction, the boundedness for such operators on Triebel-Lizorkin...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 18; no. 1; pp. 127 - 146
Main Authors Liu, Feng, Wu, Huoxiong
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.02.2014
Subjects
Abstract spaces
Mathematical functions
Mathematical integrals
Polynomials
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ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/tjm.18.2014.3147

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Summary:This paper is devoted to studying the singular integral operators associated to polynomial mappings as well as the corresponding compound submanifolds. By imposing a restrictive condition on the kernels of the operators in the radial direction, the boundedness for such operators on Triebel-Lizorkin spaces and Besov spaces are established, provided that the kernels satisfy a rather weak size condition on the unit sphere, which is distinct from the Hardy space functions. Some previous results are essentially improved and generalized. 2010Mathematics Subject Classification: 42B20, 42B25. Key words and phrases: Singular integrals, Rough kernels, Triebel-Lizorkin spaces, Besov spaces, Vectorvalued norm inequalities, Compound submanifolds.
ISSN:1027-5487
2224-6851
2224-6851
DOI:10.11650/tjm.18.2014.3147