Note on Weighted Bohr's Inequality

Abstract

In this paper, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions ${\mathcal{B}}^{\prime }$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$ where $h\in {\mathcal{B}}^{\prime }.$ Finally we give a new generalization of the Bohr's inequality for the class of analytic functions subordinate to univalent functions and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$ where $h$ is subordinated to some analytic function.

10 pages. This paper is to appear in Lobachevskii Journal of Mathematics