Twisted Orlicz algebras, I
Volume 236 / 2017
Abstract
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.
