Bohr radius for locally univalent harmonic mappings

By Ilgiz R. Kayumov, Saminathan Ponnusamy, Nail Shakirov. 2017

114 citations recorded by the source corpus.

We consider the class of all sense‐preserving harmonic mappings f=h+g¯ of the unit disk D , where h and g are analytic with g(0)=0 , and determine the Bohr radius if any one of the following conditions holds: 1.h is bounded in D . 2.h satisfies the condition Re h(z)≤1 in D with h(0)>0 . 3.both h and g are bounded in D . 4.h is bounded and g′(0)=0 . We also consider the problem of determining the Bohr radius when the supremum of the modulus of the dilatation of f in D is strictly less than 1. In addition, we determine the Bohr radius for the space B of analytic Bloch functions and the space BH of harmonic Bloch functions. The paper concludes with two conjectures.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ceb5656241f2da385cdc8c12ecce43364f31e829

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Bohr Radius for Subordination and K-quasiconformal Harmonic Mappings (2019, background): “For certain other results on harmonic Bohr’s inequality, we refer to [9, 16].”
On the Bohr inequality with a fixed zero coefficient (2019, background): “[21] investigated Bohr’s radius for locally univalent planar harmonic mappings.”