Nonabelian ramified coverings and $L^p$-boundedness of Bergman projections in ${\mathbb{C}}^2$

Abstract

In this work we explore the theme of $L^p$-boundedness of Bergman projections of domains that can be covered, in the sense of ramified coverings, by "nice" domains (e.g. strictly pseudoconvex domains with real analytic boundary). In particular, we focus on two-dimensional normal ramified coverings whose covering group is a finite unitary reflection group. In an infinite family of examples we are able to prove $L^p$-boundedness of the Bergman projection for every $p\in (1,\infty )$.

arXiv comment24 pages

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Cited by in corpus (2)

• $L^p$ regularity of the Bergman projection on the symmetrized polydisc
• The weighted Bergman spaces and complex reflection groups