Bohr Inequalities for Certain Classes of Harmonic Mappings.

Bohr's classical theorem and its generalizations are now active areas of research and have been the source of investigations in numerous function spaces. For harmonic mappings of the form f = h + g ¯ , we obtain an improved version of Bohr inequality for K-quasiregular harmonic mappings in the shifted disk Ω γ = { z ∈ C : | z + γ 1 - γ | < 1 1 - γ , γ ∈ [ 0 , 1) } which contains the unit disk D . In addition, we obtain sharp Bohr inequalities for class of K-quasiconformal harmonic mappings with bounded analytic part. [ABSTRACT FROM AUTHOR]