Multipliers of $\pmb{A}_{\pmb{p}}\pmb{((0,} \pmb{\infty}\pmb{))}$ with order convolution

Abstract

The aim of this paper is to study the multipliers from $A_{r}(I)$ to $A_{p}(I), r \ne p$, where $I=(0,\infty)$ is the locally compact topological semigroup with multiplication max and usual topology and $A_{r}(I) = \{f \in L_{1}(I)\hbox{:} \hat{f} \in L_{r}(\hat{I})\}$ with norm $|||f|||_{r} = \|f\|_{1} + \|\hat{f}\|_{r}$.