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LIPSCHITZ SPACES AND BOUNDED MEAN OSCILLATION OF HARMONIC MAPPINGS

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 18 Jan 2013Embargo end date: 01 Jan 2012Publisher:Cambridge University Press (CUP)Journal:Bulletin of the Australian Mathematical Society, volume 88, pages 143-157 (issn: 0004-9727, eissn: 1755-1633,

Authors: Sh. Chen; Saminathan Ponnusamy; Matti Vuorinen; X. Wang;

doi: 10.1017/s0004972712000998 , 10.48550/arxiv.1202.2183

arXiv: http://arxiv.org/abs/1202.2183

LIPSCHITZ SPACES AND BOUNDED MEAN OSCILLATION OF HARMONIC MAPPINGS

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Abstract

AbstractWe first study the bounded mean oscillation of planar harmonic mappings. Then we establish a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings. Finally, we obtain sharp estimates on the Lipschitz number of planar harmonic mappings in terms of the bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to$BM{O}_{2} $as a Banach space.

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Keywords

30H10, 30H30 (Primary) 30C20, 30C45 (Secondary), Mathematics - Complex Variables, ta111, FOS: Mathematics, Complex Variables (math.CV)

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