Generalized Hilbert matrix operators acting on Bergman spaces
In this article, we study the generalized Hilbert matrix operator Γ μ acting on the Bergman spaces A p of the unit disc for 1 ≤ p < ∞ . In particular, we characterize the measures μ for which the operator Γ μ 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 Γ μ is compact by calculating its exact essential norm.
Authors
- Georgios Stylogiannis (ORCID: https://orcid.org/0000-0001-9458-1640)
- David Norrbo (ORCID: https://orcid.org/0000-0003-3198-6290)
- Vassilis Daskalogiannis (ORCID: https://orcid.org/0000-0002-9791-2713)
- Santeri Miihkinen (ORCID: https://orcid.org/0000-0002-0461-5323)
- Carlo Bellavita (ORCID: https://orcid.org/0000-0003-3136-0271)
- Jukka Virtanen
Institutions
- Statistics Finland (FI)
- University of Helsinki (FI)
- University of Eastern Finland (FI)
- Anatolia College (GR)
- Aristotle University of Thessaloniki (GR)
- University of Reading (GB)
- Universitat de Barcelona (ES)
Publication Details
- Journal
- Journal of Functional Analysis
- Published
- 2025-02-10
- DOI
- https://doi.org/10.1016/j.jfa.2025.110856
- Citations
- 4
- Primary Topic
- Holomorphic and Operator Theory
- Type
- article
- Field-Weighted Citation Impact
- 14.91
Funders
- Ministerio de Ciencia, Innovación y Universidades
- Magnus Ehrnroothin Säätiö
- Hellenic Foundation for Research and Innovation
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- Engineering and Physical Sciences Research Council