Weighted Norm Estimates and Representation Formulas for Rough Singular Integrals

Details Weighted Norm Estimates and Representation Formulas for Rough Singular Integrals Weighted Norm Estimates and Representation Formulas for Rough Singular Integrals

1998-07-16

arxiv.org/abs/math/9807085v1

Mathematics

Classical Analysis and ODEs

32 pages, 2 figures

Scientific paper

Weighted norm estimates and representation formulas are proved for non-homogeneous singular integrals with no regularity condition on the kernel and only an L log L integrability condition. The representation formulas involve averages over a star-shaped set naturally associated with the kernel. The proof of the norm estimates is based on the representation formulas, some new variations of the Hardy-Littlewood maximal function, and weighted Littlewood-Paley theory.

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