Bloch-type spaces on the upper half-plane
Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1337-1346
https://doi.org/10.4134/BKMS.b160572
Published online July 31, 2017
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
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