2017/08/18 by Kayumov, Ilgiz R, Ponnusamy, Saminathan
#30A10 #30B10 #30H05 #41A58 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 30A05 #Secondary: 40A30
paper · doi:10.48550/arxiv.1708.05578
We determine the Bohr radius for the class of all functions f of the form f(z)=∑k=1^∞ akp+m zkp+m analytic in the unit disk |z|<1 and satisfy the condition |f(z)|≤ 1 for all |z|<1. In particular, our result also contains a solution to a recent conjecture of Ali, Barnard and Solynin \citeAliBarSoly for the Bohr radius for odd analytic functions, solved by the authors in \citeKayPon1. 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.