Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2017; 54(4): 1337-1346

Online first article April 12, 2017      Printed July 31, 2017

https://doi.org/10.4134/BKMS.b160572

Copyright © The Korean Mathematical Society.

Bloch-type spaces on the upper half-plane

Xi Fu and Junding Zhang

Shaoxing University, Shanghai University

Abstract

We define Bloch-type spaces of $\mathcal{C}^1(\IH)$ on the upper half plane $\mathbb{H}$ and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator $C_\phi$ acting between two Bloch spaces. These obtained results generalize the corresponding known ones to the setting of upper half plane.

Keywords: Bloch space, majorant, composition operator

MSC numbers: 30H30, 47B33, 30D45