Substitution vector-valued integral type operators on Orlicz spaces


Zahra Moayyerizadeh




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