Transference and restriction of Fourier multipliers on Orlicz spaces

Author:

Blasco Oscar1,Üster Rüya2

Affiliation:

1. Departamento de Análisis Matemático Universitat de Valencia Burjassot Valencia Spain

2. Department of Mathematics Faculty of Science, İstanbul University İstanbul Turkey

Abstract

AbstractLet G be a locally compact abelian group with Haar measure and be Young functions. A bounded measurable function m on G is called a Fourier ‐multiplier if defined for functions in such that , extends to a bounded operator from to . We write for the space of ‐multipliers on G and study some properties of this class. We give necessary and sufficient conditions for m to be a ‐multiplier on various groups such as , and . In particular, we prove that regulated ‐multipliers defined on coincide with ‐multipliers defined on the real line with the discrete topology D, under certain assumptions involving the norm of the dilation operator acting on Orlicz spaces. Also, several transference and restriction results on multipliers acting on and are achieved.

Funder

Ministerio de Ciencia, Innovación y Universidades

Türkiye Bilimsel ve Teknolojik Araştirma Kurumu

Publisher

Wiley

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Linear and bilinear Fourier multipliers on Orlicz modulation spaces;Monatshefte für Mathematik;2024-01-30

2. Transference and Restriction of Bilinear Fourier Multipliers on Orlicz Spaces;Mediterranean Journal of Mathematics;2024-01

3. Bilinear multipliers on weighted Orlicz spaces;Georgian Mathematical Journal;2023-11-20

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