Wiener Amalgam Spaces with respect to Quasi-Banach Spaces

TL;DR

This paper extends Wiener amalgam spaces to quasi-Banach spaces on locally compact groups, providing new convolution relations and relaxing invariance assumptions, with an example on the $ax+b$ group.

Contribution

It generalizes Wiener amalgam spaces to quasi-Banach spaces and introduces new convolution relations and invariance conditions, broadening the classical theory.

Findings

Established convolution relations for Wiener amalgam spaces in the quasi-Banach setting

Relaxed the invariance assumption under right translations for the global component

Provided a detailed example on the $ax+b$ group

Abstract

We generalize the theory of Wiener amalgam spaces on locally compact groups to quasi-Banach spaces. As a main result we provide convolution relations for such spaces. Also we weaken the technical assumption that the global component is invariant under right translations, which is even new for the classical Banach space case. To illustrate our theory we discuss in detail an example on the $ax+b$ group.