Composition Operators in Hyperbolic Bloch-Type and F p , q , s Spaces

Abstract

Composition operators $C_{\phi }$ from Bloch-type ${ℬ}_{\alpha }$ spaces to $F\left(p,q,s\right)$ classes, from $F\left(p,q,s\right)$ to ${ℬ}_{\alpha }$, and from $F\left(p_1,q_1,0\right)$ to $F\left(p_2,q_2,s_2\right)$ are considered. The criteria for these operators to be bounded or compact are given. Our study also includes the corresponding hyperbolic spaces.