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arXiv · 2502.21071

Restricted type estimates on the Bergman projection of some singular domains

Debraj Chakrabarti·Zhenghui Huo
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Abstract

We obtain (weighted) restricted type estimates for the Bergman projection operator on monomial polyhedra, a class of domains generalizing the Hartogs triangle. From these estimates, we recapture $L^p$ boundedness results of the Bergman projection on these domains. On some monomial polyhedra, we also discover that the Bergman projection could fail to be of weak type $(q_*,q_*)$ where $q_*$ is the right endpoint of the interval of $L^p$-regularity of the domain.

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Debraj Chakrabarti, Zhenghui Huo. 2025-02-28. Restricted type estimates on the Bergman projection of some singular domains. https://arxiv.org/abs/2502.21071

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