The weak type $(1,p)$ for convolution operators on locally compact groups

Abstract

In this paper we provide necessary and sufficient conditions for the $\text{weak}(1,p)$ boundedness, $1<p<\infty ,$ of convolution operators on locally compact (Hausdorff) topological groups. So, we generalize a classical result due to Sobolev-Hardy-Littlewood and Stepanov. Applications to Fourier multipliers on Lie groups also are given.

References in corpus (1)

• Fourier multipliers and group von Neumann algebras