Weighted convolution inequalities for radial functions

TL;DR

This paper establishes new convolution inequalities for radially symmetric functions in weighted Lebesgue and Lorentz spaces, with applications to Riesz potentials and embeddings in radial Besov spaces.

Contribution

It introduces novel convolution inequalities for radial functions in weighted spaces and applies them to Riesz potentials and Besov space embeddings.

Findings

Convolution inequalities for radial functions in weighted Lebesgue and Lorentz spaces.

Applications to Riesz potential inequalities for radial functions.

Embedding theorems for radial Besov spaces with power weights.

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.