On radial and conical Fourier multipliers

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 to the light cone in $R^{d+1}$, where $d\ge 4$, and results on characterizations of $L^p\to L^{p,\nu }$ inequalities for convolutions with radial kernels.