The Bohr Radius of the Weighted Bloch Spaces

Ramis Sh. Khasyanov

The Bohr Radius of the Weighted Bloch Spaces

Complex Variables 2023-07-17 v1

Authors: Ramis Sh. Khasyanov

Abstract

The concept of the Bohr radius of a pair of Banach spaces is introduced. The lower estimate for the value of the Bohr radius from the Bloch space to the space of bounded functions obtained by I. Kayumov, S. Ponnusamy and N. Shakirov is slightly improved. It is shown that for any weighted Bloch space the Bohr radius is not less than $1/\sqrt{2}$ . A criterion for the sharpness of the Bohr inequality in the weighted Bloch space with $R=1 / \sqrt{2}$ is obtained. Using this criterion, the examples of the weights for which the inequality is sharp is given.

Keywords

bohr radius weighted bloch space banach space bohr inequality sharpness

Cite

@article{arxiv.2307.07028,
  title  = {The Bohr Radius of the Weighted Bloch Spaces},
  author = {Ramis Sh. Khasyanov},
  journal= {arXiv preprint arXiv:2307.07028},
  year   = {2023}
}

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