Hilbert matrix operator acting between conformally invariant spaces
Abstract In this article, we study the action of the the Hilbert matrix operator $H$ from the space of bounded analytic functions into conformally invariant Banach spaces. In particular, we describe the norm of $H$ from $H^\infty $ into $\text {BMOA}$ and we characterize the positive Borel measures $\mu $ such that $H$ is bounded from $H^\infty $ into the conformally invariant Dirichlet space $M(D_\mu )$ . For particular measures $\mu $ , we also provide the norm of $H$ from $H^\infty $ into $M(D_\mu )$ .
Authors
- Georgios Stylogiannis (ORCID: https://orcid.org/0000-0001-9458-1640)
- Carlo Bellavita (ORCID: https://orcid.org/0000-0003-3136-0271)
Institutions
- Aristotle University of Thessaloniki (GR)
- Istituto Nazionale di Alta Matematica Francesco Severi (IT)
- Universitat de Barcelona (ES)
Publication Details
- Journal
- Canadian Mathematical Bulletin
- Published
- 2024-12-12
- DOI
- https://doi.org/10.4153/s0008439524000948
- Citations
- 3
- Primary Topic
- Holomorphic and Operator Theory
- Type
- article
- Field-Weighted Citation Impact
- 2.93
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Ministerio de Ciencia e Innovación
- Hellenic Foundation for Research and Innovation
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni