Bohr's phenomenon for holomorphic and harmonic functions with lacunary series in complex Banach spaces

Abstract

We determine the sharp Bohr inequality for holomorphic functions defined on a balanced domain G of a complex Banach space X and takes values from the unit disk. Also, we investigate the Bohr-type inequalities for harmonic functions $f=h+\overline{g}$ defined on a balanced domain $G\subset X$.

Keywords:

• Bohr phenomena
• harmonic function
• holomorphic function
• lacunary series

AMS Subject Classifications:

• 32A05
• 32A10
• 32K05

Acknowledgments

The author would like to thank Prof. Swadesh Kumar Sahoo for sharing some useful papers on the multidimensional Bohr radius.

Disclosure statement

No potential conflict of interest was reported by the author(s).