Lipschitz spaces and bounded mean oscillation of harmonic mappings
Sh. Chen, S. Ponnusamy, M. Vuorinen, X. Wang
TL;DR
This paper explores the relationship between Lipschitz spaces and bounded mean oscillation in harmonic mappings, establishing sharp estimates and showing the harmonic Bloch space is isomorphic to BMO2.
Contribution
It introduces a new connection between Lipschitz-type spaces and BMO norms for harmonic mappings, with sharp estimates and isomorphism results.
Findings
Harmonic Bloch space is isomorphic to BMO2 as Banach spaces
Established a relationship between Lipschitz spaces and BMO norms for harmonic mappings
Obtained sharp estimates on Lipschitz numbers of harmonic mappings
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 as a Banach space..
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Analytic and geometric function theory · Holomorphic and Operator Theory