Notes on multipliers on weighted Orlicz spaces

Abstract

Let 𝐺 be a locally compact abelian group with Haar measure 𝜇, Φ be a Young function and 𝜔 be a weight function. In this paper, we consider the weighted Orlicz space 𝐿 Φ(𝐺, 𝜔) and we investigate the relationship between the multipliers 𝐿1(𝐺, 𝜔)-module and the multipliers on a certain Banach algebra. For this purpose, we firstly define temperate function space with respect to the weighted Orlicz space 𝐿 Φ(𝐺, 𝜔) which we denote by 𝐿 Φ𝑡(𝐺, 𝜔) and give its basic properties. Later, we define a subalgebra of the space of multipliers on 𝐿 Φ(𝐺, 𝜔) and study its basic properties. We also show that this subalgebra is isometrically isomorphic to the space of multipliers of a certain Banach algebra. Moreover, we obtain a characterization for the space of multipliers of 𝐿1(𝐺, 𝜔) ∩ 𝐿 Φ(𝐺, 𝜔).

Keywords

• multiplier
• weighted Orlicz space
• locally compact group

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