WEIGHTED α -COMPOSITION AND RELATED FUNCTION SPACES

Abstract The notion of weighted α $\alpha $ alpha -composition was introduced by Ruhan Zhao in the 1990s. In this paper, we study several analytic function spaces that are closely related to weighted α $\alpha $ alpha -composition. These include α $\alpha $ alpha -Bloch spaces, F ( p , q , s ) $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces, and Campanato spaces. We obtain derivative-free characterizations for α $\alpha $ alpha -Bloch spaces and F ( p , q , s ) $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces, which improve some previous results in the literature. We also obtain a certain version of Carleson measures for Campanato spaces and F ( p , q , s ) $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces.