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arXiv · 2302.05522

Weissler and Bernoulli type inequalities in Bergman spaces

Anton D. Baranov·Ilgiz R. Kayumov·Diana M. Khammatova·Ramis Sh. Khasyanov
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Abstract

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.

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Anton D. Baranov, Ilgiz R. Kayumov, Diana M. Khammatova, Ramis Sh. Khasyanov. 2023-02-10. Weissler and Bernoulli type inequalities in Bergman spaces. https://arxiv.org/abs/2302.05522

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