COEFFICIENT ESTIMATES, LANDAU’S THEOREM AND LIPSCHITZ-TYPE SPACES ON PLANAR HARMONIC MAPPINGS
نویسندگان
چکیده
منابع مشابه
Lipschitz Spaces and Harmonic Mappings
In [11] the author proved that every quasiconformal harmonic mapping between two Jordan domains with C, 0 < α ≤ 1, boundary is biLipschitz, providing that the domain is convex. In this paper we avoid the restriction of convexity. More precisely we prove: any quasiconformal harmonic mapping between two Jordan domains Ωj , j = 1, 2, with C, j = 1, 2 boundary is bi-Lipschitz.
متن کاملLandau's theorem for planar harmonic mappings
Landau gave a lower estimate for the radius of a schlicht disk centered at the origin and contained in the image of the unit disk under a bounded holomorphic function f normalized by f(0) = f ′(0)− 1 = 1. Chen, Gauthier, and Hengartner established analogous versions for bounded harmonic functions. We improve upon their estimates.
متن کاملPlanar Harmonic Univalent and Related Mappings
The theory of harmonic univalent mappings has become a very popular research topic in recent years. The aim of this expository article is to present a guided tour of the planar harmonic univalent and related mappings with emphasis on recent results and open problems and, in particular, to look at the harmonic analogues of the theory of analytic univalent functions in the unit disc.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2013
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788713000608