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In this paper, we prove that  σ -compactness of a locally compact group  G  is a necessary condition for the weighted Orlicz space    to be a convolution algebra, and for a class of Orlicz spaces we give an equivalent condition. Also, we show that if    is   -invariant, then there exists a constant  c &gt;  0 such that Φ( ω ( st ))  ≤ c ω ( s ) ωΦ  ( t ) for locally a.e.  s ,  t  ∈  G , where  ωΦ  is a locally integrable function satisfying an inclusion property.

quaestiones mathematicae

L                           ω                           1                                                             -invariant weighted Orlicz spaces