Results on weighted norm inequalities for multipliers
Authors:
Douglas S. Kurtz and Richard L. Wheeden
Journal:
Trans. Amer. Math. Soc. 255 (1979), 343-362
MSC:
Primary 42A45; Secondary 42B20
DOI:
https://doi.org/10.1090/S0002-9947-1979-0542885-8
MathSciNet review:
542885
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Abstract | References | Similar Articles | Additional Information
Abstract: Weighted -norm inequalities are derived for multiplier operators on Euclidean space. The multipliers are assumed to satisfy conditions of the Hörmander-Mikhlin type, and the weight functions are generally required to satisfy conditions more restrictive than
which depend on the degree of differentiability of the multiplier. For weights which are powers of
, sharp results are obtained which indicate such restrictions are necessary. The method of proof is based on the function
of C. Fefferman and E. Stein rather than on Littlewood-Paley theory. The method also yields results for singular integral operators.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1979-0542885-8
Article copyright:
© Copyright 1979
American Mathematical Society