Project description
Study explores complex Bergman spaces with unusual weights
Bergman spaces, consisting of analytic functions on complex domains, play a crucial role in operator theory and harmonic analysis. With the support of the Marie Skłodowska-Curie Actions programme, the LARGE BERGMAN project aims to advance understanding of large Bergman spaces, which are defined using rapidly decaying, non-doubling weights. Unlike standard cases, these weights interact less naturally with the hyperbolic geometry of the underlying domain, leaving certain theoretical questions unresolved. Researchers will explore the boundedness of the Bergman projection in weighted L^p-norms in relation to Toeplitz and little Hankel operators. They will also extend studies of localised operator classes to these large spaces. By building on established techniques, including kernel pointwise estimates and Fock-space methods, the project opens new avenues for studying non-doubling measures.
Objective
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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Keywords
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2022-PF-01
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00014 Helsinki
Finland
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