A1 Refereed original research article in a scientific journal

Lipschitz spaces and bounded mean oscillation of harmonic mappings



Authors: Chen S, Ponnusamy S, Vuorinen M, Wang X

Publication year: 2013

Journal: Bulletin of the Australian Mathematical Society

Journal name in source: Bulletin of the Australian Mathematical Society

Number in series: 1

Volume: 88

Issue: 1

First page : 143

Last page: 157

Number of pages: 15

ISSN: 0004-9727

DOI: https://doi.org/10.1017/S0004972712000998

Web address : http://api.elsevier.com/content/abstract/scopus_id:84881595697


Abstract
We 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 BMO as a Banach space. © 2012 Australian Mathematical Publishing Association Inc.



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