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.
Xi Fu and Junding Zhang
Shaoxing University, Shanghai University
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
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