Abstract
In this paper, we give some sufficient conditions for a weighted Orlicz space \(L^\Phi _w(G)\) to be a convolution Banach algebra, where G is a locally compact group and \(\Phi \) is a Young function. Also, we prove a hereditary property regarding the discrete subgroups of G. Furthermore, we show that if G be an abelian locally compact group with an open compact subgroup, \((\Phi ,\Psi )\) be a complementary pair of N-functions, and \(L^\Phi _w(G)\) be a convolution Banach algebra, then \(\frac{1}{w^*}\in L^\Psi (G)\).
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Communicated by Matthew Daws.
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Bagheri Salec, A., Tabatabaie, S.M. Some Necessary and Sufficient Conditions for Convolution Weighted Orlicz Algebras. Bull. Iran. Math. Soc. 48, 2509–2520 (2022). https://doi.org/10.1007/s41980-021-00655-y
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DOI: https://doi.org/10.1007/s41980-021-00655-y