Lipschitz spaces and bounded mean oscillation of harmonic mappings

Details Lipschitz spaces and bounded mean oscillation of harmonic mappings Lipschitz spaces and bounded mean oscillation of harmonic mappings

2012-02-10

arxiv.org/abs/1202.2183v1

Mathematics

Complex Variables

13, pages; submitted to a journal

Scientific paper

In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on Lipschitz number of planar harmonic mappings in terms of bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to $BMO_{2}$ as a Banach space.

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