Weighted composition operators between $L^p$-spaces
Bull. Korean Math. Soc. 2005 Vol. 42, No. 2, 369-378 Printed June 1, 2005
M. R. Jabbarzadeh University of Tabriz, University of Tabriz
Abstract : In this paper we will consider the weighted composition operator $W=uC_\varphi$ between two different $L^p(X,\Sigma, \mu)$ spaces, generated by measurable and non-singular transformations $\varphi$ from $X$ into itself and measurable functions $u$ on $X$. We characterize the functions $u$ and transformations $\varphi$ that induce weighted composition operators between $L^p$-spaces by using some properties of conditional expectation operator, pair ($u$,$\varphi$) and the measure space $(X,\Sigma,\mu)$. Also, Fredholmness of these type operators will be investigated.