Some remarks on the $L^P$-$L^q$ boundedness of $uC_{varphi}$

Abstract

In this paper we will consider the weighted composition operators between two different $L^P$- spaces and then we characterize the functions u and transformations $varphi$ that induce weighted composition operator $uC_{varphi}$ between $L^p(X,Sigma, mu)$-spaces by using some properties of conditional expectation operator, pair (u, $varphi$) and the measure space $(X,Sigma,mu)$.