‎substitution vector-valued integral type operators on Orlicz spaces‎

Abstract

In this paper, we consider some fundamental properties of a substitution vector-valued integral operator  from Orlicz space Lθ(µ) to Hilbert
space H by the language of conditional expectation operators. First, we present
necessary and sufficient conditions for boundedness and compactness these operators from Lθ(µ) to H. Next, we investigate the problem of conditions on the generating Young functions, the functions u, ’ and..  , under which operator these operators ’ is of closed range or finite rank. Finally, we determine the lower and
upper estimates for the essential norm of the substitution vector-valued integral operator on Orlicz spaces under certain conditions.