Characterization of vector-valued $L^1$-$L^p$ multipliers for Weyl transform

TL;DR

This paper characterizes Weyl multipliers acting on vector-valued $L^1$-$L^p$ spaces associated with a complex Banach algebra, extending the understanding of these operators in harmonic analysis.

Contribution

It provides a new characterization of Weyl multipliers for vector-valued $L^1$-$L^p$ spaces with Banach algebra values, under bounded approximate identity assumptions.

Findings

Characterization of Weyl multipliers for vector-valued $L^1$-$L^p$ spaces.

Extension of multiplier theory to Banach algebra-valued functions.

Results applicable for $1 \,\leq p < \infty$.

Abstract

In this article, we will characterize Weyl multipliers for the pair $(L^1(G \times \widehat{G}; A), L^p(G \times \widehat{G};A))$, for $1 \leq p< \infty$, under the assumption that $A$ is a complex Banach algebra with a bounded approximate identity.