A note on weighted composition operators on \(L^p\)-spaces
The authors consider the weighted composition operators \(uC_{\phi}\) between two different \(L^p(X,\Sigma,\mu)\) spaces, generated by measurable and non-singular transformations \(\phi\) from \(X\) into itself and measurable functions \(u\) on \(X.\) They characterize the functions \(u\) and transformations \(\phi\) that induce weighted composition operators between \(L^p\)-spaces by using some properties of the conditional expectation operator, the pair \((u, \phi)\) and the measure space \((X,\Sigma,\mu)\). Some other properties of these types of operators are also investigated.
scientific article; zbMATH DE number 2109214
scientific article