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ON HARMONIC BLOCH SPACES IN THE UNIT BALL OF ℂn
Published online by Cambridge University Press: 10 June 2011
Abstract
In this paper, our main aim is to discuss the properties of harmonic mappings in the unit ball 𝔹n. First, we characterize the harmonic Bloch spaces and the little harmonic Bloch spaces from 𝔹n to ℂ in terms of weighted Lipschitz functions. Then we prove the existence of a Landau–Bloch constant for a class of vector-valued harmonic Bloch mappings from 𝔹n to ℂn.
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- Research Article
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- Copyright © Australian Mathematical Publishing Association Inc. 2011
Footnotes
The research was partly supported by NSF of China (No. 11071063), Hunan Provincial Innovation Foundation for Postgraduate (No. 125000-4113) and the Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province.
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