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
Cited by
3 articles.
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