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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
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 $\left | x \right |$, sharp results are obtained which indicate such restrictions are necessary. The method of proof is based on the function ${f^\# }$ 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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Article copyright: © Copyright 1979 American Mathematical Society