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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Iterated Littlewood-Paley functions and a multiplier theorem


Author: W. R. Madych
Journal: Proc. Amer. Math. Soc. 45 (1974), 325-331
MSC: Primary 42A92; Secondary 42A18
DOI: https://doi.org/10.1090/S0002-9939-1974-0355475-8
MathSciNet review: 0355475
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Abstract: A sufficient condition for a bounded function to be a multiplier of Fourier transforms on $ {L^p}({R^n}),1 < p < \infty $, is established. The classical case of Marcinkiewicz is properly included. The main tools used in obtaining this result are iterated variants of the classical LittlewoodPaley functions together with an $ {L^p}$ estimate on certain maximal functions closely related to strong differentiability of multiple integrals.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0355475-8
Article copyright: © Copyright 1974 American Mathematical Society