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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: Weighted $ {L^p}$-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 $ {A_p}$ which depend on the degree of differentiability of the multiplier. For weights which are powers of $ \left\vert x \right\vert$, sharp results are obtained which indicate such restrictions are necessary. The method of proof is based on the function $ {f^\char93 }$ 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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DOI: https://doi.org/10.1090/S0002-9947-1979-0542885-8
Article copyright: © Copyright 1979 American Mathematical Society

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