Transference for radial multipliers and dimension free estimates

Auscher, P.; Carro, M. J.

doi:10.1090/S0002-9947-1994-1152319-9

Transference for radial multipliers and dimension free estimates
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by P. Auscher and M. J. Carro PDF

Trans. Amer. Math. Soc. 342 (1994), 575-593 Request permission

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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