Research Article

L ω 1 -invariant weighted Orlicz spaces

Published in: Quaestiones Mathematicae
Volume 46 , issue 9 , 2023 , pages: 1765–1776

DOI: 10.2989/16073606.2022.2114961

Author(s): AliReza Bagheri Salec University of Qom, Iran , Seyyed Mohammad Tabatabaie University of Qom, Iran

Keywords: Primary: Primary: 46E30 , Secondary: Secondary: 43A15 , Locally compact group , σ-compact group , convolution algebra , weighted Orlicz space , semimultiplicative weight function

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Abstract

In this paper, we prove that σ-compactness of a locally compact group G is a necessary condition for the weighted Orlicz space to be a convolution algebra, and for a class of Orlicz spaces we give an equivalent condition. Also, we show that if is -invariant, then there exists a constant c > 0 such that Φ(ω(st)) ≤ c ω(s)ω _Φ (t) for locally a.e. s, t ∈ G, where ω _Φ is a locally integrable function satisfying an inclusion property.

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