Products of differentiation and composition operators on the Bloch space

Abstract

We consider linear product operators \({DC_{\phi}}\) and \({C_{\phi}D^{m}}\) acting on the Bloch space, where \({C_{\phi}}\) is the composition operator and Dm is the differentiation operator. The compactness criteria of the operators \({DC_{\phi}}\) and \({C_{\phi}D^{m}}\) on the Bloch space are established in terms of the norms of \({\phi^n}\) in the Bloch space.