Twisted Orlicz algebras, I

Volume 236 / 2017

Serap Öztop, Ebrahim Samei Studia Mathematica 236 (2017), 271-296 MSC: Primary 46E30, 43A15, 43A20; Secondary 20J06. DOI: 10.4064/sm8562-9-2016 Published online: 23 December 2016


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.


  • Serap ÖztopDepartment of Mathematics
    Faculty of Science
    Istanbul University
    Istanbul, Turkey
  • Ebrahim SameiDepartment of Mathematics and Statistics
    University of Saskatchewan
    Saskatoon, Saskatchewan, S7N 5E6, Canada

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