Norm estimates for the Hilbert matrix operator on weighted Bergman spaces
Norrbo, D.
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.jmaa.2025.129408 Abstract/SummaryWe study the Hilbert matrix operator H and a related integral operator T acting on the standard weighted Bergman spaces Ap α. We obtain an upper bound for T, which yields the smallest currently known explicit upper bound for the norm of H for −1 <α< 0 and 2 + α<p< 2(2 + α). We also calculate the essential norm for all p > 2 + α > 1, extending a part of the main result in [Adv. Math. 408 (2022) 108598] to the standard unbounded weights. It is worth mentioning that except for an application of Minkowski’s inequality, the norm estimates obtained for T are sharp.
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