Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2015; 52(3): 751-759

Printed May 31, 2015

https://doi.org/10.4134/BKMS.2015.52.3.751

Copyright © The Korean Mathematical Society.

New characterizations of composition operators between Bloch type spaces in the unit ball

Zhong-Shan Fang and Ze-Hua Zhou

Tianjin Polytechnic University, Tianjin University

Abstract

In this paper, we give new characterizations of the boundedness and compactness of composition operators $C_\varphi$ between Bloch type spaces in the unit ball $\mathbb{B}^n,$ in terms of the power of the components of $\varphi,$ where $\varphi$ is a holomorphic self-map of $\mathbb{B}^n.$

Keywords: composition operator, compactness, Bloch type spaces, unit ball, several complex variables

MSC numbers: Primary 47B38, 32A18; Secondary 47B33, 32A10, 32H02