Abstract
In this paper, we consider some fundamental properties of a substitution vector-valued integral operator Tu? from Orlicz space L?(?) to Hilbert space H by the language of conditional expectation operators. First, we present necessary and sufficient conditions for boundedness and compactness Tu? from L?(?) to H. Next, we investigate the problem of conditions on the generating Young functions, the functions u, ? and h = d(? ? ?-1)/d?, under which operator Tu? is of closed range or finite rank. Finally, we determine the lower and upper estimates for the essential norm of Tu? on Orlicz spaces under certain conditions.
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