Twisted Orlicz algebras, I

Serap Öztop¹ ; Ebrahim Samei²

¹ Department of Mathematics Faculty of Science Istanbul University Istanbul, Turkey
² Department of Mathematics and Statistics University of Saskatchewan Saskatoon, Saskatchewan, S7N 5E6, Canada

Studia Mathematica, Tome 236 (2017) no. 3, pp. 271-296

Résumé

Let $G$ be a locally compact group, let $\varOmega :G\times G\to \mathbb {C}^*$ be a 2-cocycle, and let $\varPhi $ be a Young function. In this paper, we consider the Orlicz space $L^\varPhi (G)$ and investigate its algebraic properties under the twisted convolution $\circledast $ coming from $\varOmega $. We find sufficient conditions under which $(L^\varPhi (G),\circledast )$ becomes a Banach algebra or a Banach $*$-algebra; we then call it a twisted Orlicz algebra. Furthermore, we study its harmonic analysis properties, such as symmetry, existence of functional calculus, regularity, and the Wiener property, mostly when $G$ is a compactly generated group of polynomial growth. We apply our methods to several important classes of polynomial as well as subexponential weights, and demonstrate that our results could be applied to a variety of cases.

Détail

DOI : 10.4064/sm8562-9-2016

Keywords: locally compact group varomega times mathbb * cocycle varphi young function paper consider orlicz space varphi investigate its algebraic properties under twisted convolution circledast coming varomega sufficient conditions under which varphi circledast becomes banach algebra banach * algebra call twisted orlicz algebra furthermore study its harmonic analysis properties symmetry existence functional calculus regularity wiener property mostly compactly generated group polynomial growth apply methods several important classes polynomial subexponential weights demonstrate results could applied variety cases