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Rough Singular Integral Operators Along Polynomial Curves

Posted on:2009-01-01Degree:MasterType:Thesis
Country:ChinaCandidate:L MaFull Text:PDF
GTID:2120360272490373Subject:Basic mathematics
Abstract/Summary:
This desertation is devoted to studying rough singular integral operators associated to polynomial curves. It consists of two chapters. The firt chapter is concerning with the one-parameter singular integrals and the second one deals with the multiple-parameter singular integrals. Some rather weak size conditions both along the radial direction and on sperical surface, which imply the L~p boundedness of these singular integral operators for some fixed p(l < p <∞), are obtained.
Keywords/Search Tags:singular integrals, polynomial curves, maximal op erator, product domain, rough kernel, Littlewood-Paley theory, Fourier transform estimate
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