Weighted Composition Operators on Weighted Lorentz-Karamata Spaces

Abstract

In this paper, a characterization of the non-singular measurable transformations T from X into itself and complex-valued measurable functions u on X inducing weighted composition operators is obtained and subsequently their compactness and closedness of the range on the weighted Lorentz-Karamata spaces L-p,q;b(w) (X, Sigma, mu) are completely identified where (X, Sigma, mu) is a sigma-finite measure space and 1 < p <= infinity, 1 <= q <= infinity.