Weighted convolution inequalities for radial functions

Abstract

We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of radial functions in weighted Lorentz spaces and embedding theorems for radial Besov spaces with power weights.

arXiv comment14 pages. New section with applications to weighted embedding theorems for radial Besov spaces added