, Volume 21, Issue 1, pp 96-117
Date: 10 Aug 2010

On Radial and Conical Fourier Multipliers

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Abstract

We investigate connections between radial Fourier multipliers on ℝ d and certain conical Fourier multipliers on ℝ d+1. As an application we obtain a new weak type endpoint bound for the Bochner–Riesz multipliers associated with the light cone in ℝ d+1, where d≥4, and results on characterizations of L p L p inequalities for convolutions with radial kernels.

Communicated by Loukas Grafakos.
Y.H. supported by Korea Research Foundation Grant KRF-2008-357-C00002 and National Research Foundation of Korea Grant NRF-2009-0094068. F.N. supported in part by NSF grant 0800243. A.S. supported in part by NSF grant 0652890.