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Coefficient estimates, Landau’s theorem and Lipschitz-type spaces on planar harmonic mappings. (English) Zbl 1290.30063

Summary: We investigate the properties of locally univalent and multivalent planar harmonic mappings. First, we discuss coefficient estimates and Landau’s theorem for some classes of locally univalent harmonic mappings, and then we study some Lipschitz-type spaces for locally univalent and multivalent harmonic mappings.

MSC:

30H05 Spaces of bounded analytic functions of one complex variable
30H10 Hardy spaces
30H30 Bloch spaces
30C20 Conformal mappings of special domains
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C62 Quasiconformal mappings in the complex plane
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
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