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Transactions of the American Mathematical Society

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



Transference for radial multipliers and dimension free estimates

Authors: P. Auscher and M. J. Carro
Journal: Trans. Amer. Math. Soc. 342 (1994), 575-593
MSC: Primary 42B15; Secondary 42B25
MathSciNet review: 1152319
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Abstract: For a large class of radial multipliers on $ {L^p}({{\mathbf{R}}^{\mathbf{n}}})$, we obtain bounds that do not depend on the dimension n. These estimates apply to well-known multiplier operators and also give another proof of the boundedness of the Hardy-Littlewood maximal function over Euclidean balls on $ {L^p}({{\mathbf{R}}^{\mathbf{n}}})$, $ p \geq 2$, with constant independent of the dimension. The proof is based on the corresponding result for the Riesz transforms and the method of rotations.

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Keywords: Radial multipliers, transference
Article copyright: © Copyright 1994 American Mathematical Society