Extensions of Weak-Type Multipliers

Abstract

In this paper we prove that if $\Lambda \in M_p({\mathbb{R}}^N)$ and has compact support then $\Lambda$ is a weak summability kernel for $1<p<\infty$, where $M_p({\mathbb{R}}^N)$ is the space of multipliers of $L^p({\mathbb{R}}^N)$.