Radial Fourier multipliers in high dimensions

Abstract

Given a fixed p≠2, we prove a simple and effective characterization of all radial multipliers of $ \mathcal{F}{L^p}\left( {{\mathbb{R}^d}} \right) $, provided that the dimension d is sufficiently large. The method also yields new Lq space-time regularity results for solutions of the wave equation in high dimensions.