LARGE BERGMAN
Financiado
Toeplitz and related operators in large Bergman spaces
We consider operator theory in Bergman spaces consisting of analytic functions on complex domains. The aim is to extend known, central results of standard Bergman spaces to the case of large spaces, which are naturally defined by...
We consider operator theory in Bergman spaces consisting of analytic functions on complex domains. The aim is to extend known, central results of standard Bergman spaces to the case of large spaces, which are naturally defined by using rapidly decaying, non-doubling weights. The need of weighted estimates is as apparent as anywhere in harmonic analysis and applications. In the context of Bergman spaces, the case of non-doubling weights is still partially open due to the fact that such weights are not so naturally related with the hyperbolic metric of the underlying domain. In this context we plan to consider questions of boundedness of the Bergman projection in weighted L^p-norms in relation to the boundedness of Toeplitz and also little Hankel operators.
In the case of standard weighted Bergman spaces there is a well-known connection of the theory to the deformation quantization.
Another topic of recent interest is formed by the so called localized operator classes. We aim to extend these studies to the case of
large Bergman spaces.
The methodology comes from the earlier joint works of the researcher and a number of well known experts in the area, on the topic
of pointwise estimates of the Bergman kernel among others, and from the techniques of the supervisor and W.Lusky, as well as Fock-space
methods, which are naturally related to nondoubling measures.
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Duración del proyecto: 25 meses
Fecha Inicio: 2023-03-20
Fecha Fin: 2025-04-30
Fecha Fin: 2025-04-30
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2023-03-20
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
HORIZON-MSCA-2022-PF-01-01:
MSCA Postdoctoral Fellowships 2022
Cerrada
hace 2 años
Presupuesto
El presupuesto total del proyecto asciende a
216K€
Líder del proyecto
HELSINGIN YLIOPISTO
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
N.D. |
Participante