Composition operators in Orlicz spaces

Abstract

Composition operators C t between Orlicz spaces V (n, S, fi) generated by measurable and nonsingular transformations r from Q into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping T, the function ip and the measure space (fi, E, n). These results generalize earlier results known for L p -spaces.2000 Mathematics subject classification: primary 47B33,46E30; secondary 47B07, 46B70.

Composition operators on Lorentz spaces

“…There is a vast literature for composition operators on measurable function spaces and their applications, one can refer to [4,5,6,8,9,11,12,16,18,19,20] The main aim of this paper is to study Predholmn property, isometry, invertibility of composition operators on Lorentz spaces L(p,q). In Section 2, we study the boundedness of composition operators between Lorentz spaces with different measure spaces.…”

Weighted composition operators on Orlicz-Sobolev spaces

“…Other similar references include ( [2,3,5] and [7]). In Section 2 we define the composition operator on W…”

Composition Operators on Orlicz–Lorentz Spaces

“…Condition (1.1) is sufficient for the continuity of any composition operator on rearrangement invariant space X (cf., [5]), where I = (0, ∞) with absolutely continuous norm. The group {C ϕt : t ∈ R} defined by…”

“…The study of composition operators on Lorentz spaces and Orlicz spaces has been initiated in [5], [10], [11] and [16, p-368].…”