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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Results on weighted norm inequalities for multipliers
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by Douglas S. Kurtz and Richard L. Wheeden PDF
Trans. Amer. Math. Soc. 255 (1979), 343-362 Request permission

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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Additional Information
  • © Copyright 1979 American Mathematical Society
  • 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