Weak amenability of weighted Orlicz algebras

TL;DR

This paper investigates the weak amenability of weighted Orlicz algebras on locally compact abelian groups, extending known results for weighted group algebras to a broader class of function spaces.

Contribution

It establishes conditions for weak amenability of weighted Orlicz algebras, generalizing previous results and applying to various weighted function spaces including weighted L^p-spaces.

Findings

Weak amenability characterized under new conditions

Applicable to weighted Orlicz and L^p spaces

Extends results from weighted group algebras to Orlicz algebras

Abstract

Let G be a locally compact abelian group, $\omega:G\to (0,\infty)$ be a weight, and ($\Phi$,$\Psi$) be a complementary pair of strictly increasing continuous Young functions. We show that for the weighted Orlicz algebra $L^\Phi_\omega(G)$, the weak amenability is obtained under conditions similar to the one considered by Y. Zhang for weighted group algebras. Our methods can be applied to various families of weighted Orlicz algebras, including weighted $L^p$-spaces.