Bohr's inequality for analytic functions ${\sum }_k{b}_k{z}^{kp+m}$ and harmonic functions

Abstract

We determine the Bohr radius for the class of all functions $f$ of the form $f(z)={\sum }_{k=1}^{\infty }{a}_{kp+m}{z}^{kp+m}$ analytic in the unit disk $|z|<1$ and satisfy the condition $|f(z)|\le 1$ for all $|z|<1$. In particular, our result also contains a solution to a recent conjecture of Ali, Barnard and Solynin \cite{AliBarSoly} for the Bohr radius for odd analytic functions, solved by the authors in \cite{KayPon1}. We consider a more flexible approach by introducing the $p$-Bohr radius for harmonic functions which in turn contains the classical Bohr radius as special case. Also, we prove several other new results and discuss $p$-Bohr radius for the class of odd harmonic bounded functions.

13 pages; The article is with a journal for several months

References in corpus (1)

• Bohr inequality for odd analytic functions