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arXiv · 2211.03655

Hypercontractive inequalities for weighted Bergman spaces

Petar Melentijević
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Abstract

\begin{abstract} We obtain sharp $L^p\rightarrow L^q$ hypercontractive inequalities for the weighted Bergman spaces on the unit disk $\mathbb{D}$ with the usual weights \\ $\frac{\alpha-1}{\pi}(1-|z|^2)^{\alpha-2},\alpha>1$ for $q\geq 2,$ thus solving an interesting case of a problem from \cite{JANSON}. We also give some estimates for $0<q<2.$ \end{abstract}

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Petar Melentijević. 2022-11-07. Hypercontractive inequalities for weighted Bergman spaces. https://doi.org/10.1112/blms.12883

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