Weighted Composition Operators on Bicomplex Lorentz Spaces With Their Characterization and Properties

Abstract

This article presents a characterization of non-singular measurable transformation, denoted as T, mapping from Omega to itself, along with bicomplex-valued BC-measurable function u defined on Omega, which induces a weighted composition operator. The study then proceeds to fully identify their D-compactness and D-closedness within the range of bicomplex Lorentz spaces denoted as L (BC)(p q), Omega, , M theta theta( ), where ( Omega, , M theta ) represents a sigma-finite complete BC-measure space, theta = + theta 1e1 theta 2e2 is a BC-measure, and the parameters satisfy 1 < <=infinity p , 1 <= <=infinity