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Generalized Hilbert matrix operators acting on Bergman spaces

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Bellavita, C., Daskalogiannis, V., Miihkinen, S., Norrbo, D., Stylogiannis, G. and Virtanen, J. (2025) Generalized Hilbert matrix operators acting on Bergman spaces. Journal of Functional Analysis, 288 (9). 110856. ISSN 0022-1236 doi: 10.1016/j.jfa.2025.110856

Abstract/Summary

In this article, we study the generalized Hilbert matrix operator Γμ acting on the Bergman spaces Ap of the unit disc for 1 ≤ p < ∞. In particular, we characterize the measures μ for which the operator Γμ is bounded, determine the exact value of the norm for p ≥ 4, and provide norm estimates for the other values of p. Additionally, we observe an unexpected behavior in the case p = 2. Finally, we characterize the measures μ for which Γμ is compact by calculating its exact essential norm.

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Item Type Article
URI https://centaur.reading.ac.uk/id/eprint/120720
Identification Number/DOI 10.1016/j.jfa.2025.110856
Refereed Yes
Divisions Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher Elsevier
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