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Let $G$ be a locally compact group, $\Phi$ be a Young function, and denote by $L^{\Phi}(G)$ the associated Orlicz space. Orlicz spaces are known as natural generalizations of $L^{p}-$ spaces. Let $\Omega: G \times G \rightarrow \mathbb{C} \backslash\{0\}$ be a 2 -cocyle. We consider the twisted convolution over the Orlicz space $L^{\phi}(G)$ coming from $\Omega .$ This talk is a survey of results on Banach algebra and Banach module structures of Orlicz spaces on $G$ that we have obtained recently in collaboration with our colleagues. Our approach allows us to systematically and simultaneously study twisted convolutions as well as weighted spaces. We apply our method in the form of twisted Orlicz algebras on compactly generated groups of polynomial growth.

This presentation is based on joint works with Ebrahim Samei and Varvara Shepelska of University of Saskatchewan, Canada.
 

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1608637155824?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d