Norm estimates for the Hilbert matrix operator on weighted Bergman spaces

Norrbo, D. ORCID: https://orcid.org/0000-0003-3198-6290 (2025) Norm estimates for the Hilbert matrix operator on weighted Bergman spaces. Journal of Mathematical Analysis and Applications, 548 (2). 129408. ISSN 1096-0813 doi: 10.1016/j.jmaa.2025.129408

Abstract/Summary

We 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/121780
Identification Number/DOI	10.1016/j.jmaa.2025.129408
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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