Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2017; 32(3): 567-578

Online first article January 18, 2017      Printed July 31, 2017

https://doi.org/10.4134/CKMS.c160134

Copyright © The Korean Mathematical Society.

Extended Ces\`{a}ro Operators between $\alpha$-Bloch spaces and $Q_{K}$ spaces

Shunlai Wang and Taizhong Zhang

Nanjing University of Information Science and Technology, Nanjing University of Information Science and Technology

Abstract

Many scholars studied the boundedness of Ces\`{a}ro operators between $Q_K$ spaces and Bloch spaces of holomorphic functions in the unit disc in the complex plane, however, they did not describe the compactness. Let $0<\alpha<+\infty$, $K(r)$ be right continuous nondecreasing functions on $(0,+\infty)$ and satisfy $$\int_{0}^{1\over e}K(\log{1\over r})rdr<+\infty.$$Suppose $g$ is a holomorphic function in the unit disk. In this paper, some sufficient and necessary conditions for the extended Ces\`{a}ro operators $T_g$ between $\alpha$-Bloch spaces and $Q_K$ spaces in the unit disc to be bounded and compact are obtained.

Keywords: extended ces\`{a}ro operators, $\alpha$-Bloch spaces, $Q_K$ spaces, boundedness, compactness

MSC numbers: Primary 30H25, 30H30, 47B33, 47B38