On Radial and Conical Fourier Multipliers

Abstract

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