arXiv subjects

Ramis Sh. Khasyanov

Publications and source records attributed to Ramis Sh. Khasyanov.

2 recordsLinked to original sources

arXiv2023

The Bohr Radius of the Weighted Bloch Spaces

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.

math.CV↗

arXiv2023

Weissler and Bernoulli type inequalities in Bergman spaces

We consider Weissler type inequalities for Bergman spaces with general radial weights and give conditions on the weight $w$ in terms of its moments ensuring that $\|f_r\|_{A^{2n}(w)}\leq \|f\|_{A^2(w)}$ whenever $n\in \mathbb{N}$ and $0< r\le 1/\sqrt{n}$. For noninteger exponents a special case of this inequality is proved which can be considered as a certain analog of the Bernoulli inequality. An example of a monotonic weight is constructed for which these inequalities are no longer true.

math.CV↗