\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}Comment: 5 pages; accepted for publication in Bulletin of London Mathematical Societ
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MSC 2010: 30C45, 30C50The object of this paper is to obtain sharp results involving coefficient boun...
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AbstractSome new results that provide refinements and reverses of the Cauchy–Bunyakovsky–Schwarz (CB...
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