GENERALIZED WEIGHTED COMPOSITION OPERATORS FROM AREA NEVANLINNA SPACES TO BLOCH-TYPE SPACES

Abstract

Let $H({\mathbb D})$ denote the class of all analytic functions on the open unit disk ${\mathbb D}$ of ${\mathbb C}$. Let $\varphi$ be an analytic self-map of ${\mathbb D}$ and $u \in H({\mathbb D})$. The generalized weighted composition operator is defined by $$ D^n_{\varphi,u} f = uf^{(n)} \circ \varphi, \quad f \in H({\mathbb D}).$$ The boundedness and compactness of generalized weighted composition operators from area Nevanlinna spaces to Bloch-type spaces and little Bloch-type spaces are characterized in this paper.