Composition operators in hyperbolic general Besov-type spaces

A. El-Sayed Ahmed; M. A. Bakhit

doi:10.4067/S0719-06462013000300003

Authors

A. El-Sayed Ahmed Taif University, Faculty of Science, Mathematics, Department, box 888 El-Hawiyah, El-Taif 5700, Saudi Arabia.
M. A. Bakhit Department of Mathematics, Faculty of Science, Assiut Branch, Al-Azhar University, Assiut 32861, Egypt.

DOI:

https://doi.org/10.4067/S0719-06462013000300003

Keywords:

Hyperbolic classes, composition operators, Lipschitz continuous, Î±-Bloch space, Fâˆ—(p, q, s) class

Abstract

In this paper we introduce natural metrics in the hyperbolic Î±-Bloch and hyperbolic general Besov-type classes Fâˆ—(p, q, s). These classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, compact composition operators C_Ï† acting from the hyperbolic Î±-Bloch class to the class Fâˆ—(p, q, s) are characterized by conditions depending on an analytic self-map Ï† : D â†’ D.