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Bergman projection and BMO in hyperbolic metric: improvement of classical result.
dc.contributor.author | Rättyä, Jouni | |
dc.contributor.author | Peláez-Márquez, José Ángel | |
dc.date.accessioned | 2025-01-30T08:10:06Z | |
dc.date.available | 2025-01-30T08:10:06Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Peláez, J.Á., Rättyä, J. Bergman projection and BMO in hyperbolic metric: improvement of classical result. Math. Z. 305, 19 (2023). https://doi.org/10.1007/s00209-023-03343-1 | es_ES |
dc.identifier.uri | https://hdl.handle.net/10630/37351 | |
dc.description.abstract | The Bergman projection $P_\alpha$, induced by a standard radial weight, is bounded and onto from $L^\infty$ to the Bloch space $\mathcal{B}$. However, $P_\alpha: L^\infty\to \mathcal{B}$ is not a projection. This fact can be emended via the boundedness of the operator $P_\alpha:\BMO_2(\Delta)\to\mathcal{B}$, where $\BMO_2(\Delta)$ is the space of functions of bounded mean oscillation in the Bergman metric. We consider the Bergman projection $P_\omega$ and the space $\BMO_{\omega,p}(\Delta)$ of functions of bounded mean oscillation induced by $1<p<\infty$ and a radial weight $\omega\in\mathcal{M}$. Here $\mathcal{M}$ is a wide class of radial weights defined by means of moments of the weight, and it contains the standard and the exponential-type weights. We describe the weights such that $P_\omega:\BMO_{\omega,p}(\Delta)\to\mathcal{B}$ is bounded. They coincide with the weights for which $P_\omega: L^\infty \to \mathcal{B}$ is bounded and onto. This result seems to be new even for the standard radial weights when $p\ne2$. | es_ES |
dc.description.sponsorship | The research was supported in part by La Junta de Andalucía, project FQM210, and Vilho, Yrjö ja Kalle Väisälä foundation of Finnish Academy of Science and Letters. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Springer Nature | es_ES |
dc.rights | Attribution 4.0 Internacional | |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | Funciones de variable compleja | es_ES |
dc.subject.other | Bergman projection | es_ES |
dc.subject.other | Bergman metric | es_ES |
dc.subject.other | Bergman space | es_ES |
dc.subject.other | Bloch space | es_ES |
dc.subject.other | Doubling weight | es_ES |
dc.subject.other | Mean oscillation | es_ES |
dc.title | Bergman projection and BMO in hyperbolic metric: improvement of classical result. | es_ES |
dc.type | journal article | es_ES |
dc.centro | Facultad de Ciencias | es_ES |
dc.identifier.doi | 10.1007/s00209-023-03343-1 | |
dc.type.hasVersion | VoR | es_ES |
dc.departamento | Análisis Matemático, Estadística e Investigación Operativa y Matemática Aplicada | |
dc.rights.accessRights | open access | es_ES |