Lipschitz spaces and bounded mean oscillation of harmonic mappings

Authors

  • Sh. Chen Hengyang Normal University
  • S. Ponnusamy Indian Institute of Technology Madras
  • M. Vuorinen University of Turku
  • X. Wang Hunan Normal University

Keywords:

Harmonic mapping, majorant, Lipschitz space, BMO_p, equivalent modulus, harmonic Bloch space, Green's theorem.

Abstract

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. 10.1017/S0004972712000998

Author Biographies

Sh. Chen, Hengyang Normal University

Department of Mathematics and Computational Science, Assistant Professor

S. Ponnusamy, Indian Institute of Technology Madras

Department of Mathematics, Professor

M. Vuorinen, University of Turku

Department of Mathematics, Professor

X. Wang, Hunan Normal University

Department of Mathematics, Professor

Published

2013-07-23

Issue

Vol. 88 No. 1 (2013)

Section

Articles
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