L^p mapping problems for Bergman projections

Abstract: This is for the most part a survey talk. I will discuss various as- pects of the following problem: for which values of $p$ is the Bergman projection of a given domain in $\mathbb C^n$ bounded on $L^p$? The answer depends heavily on the complex geometry of the domain. We will discuss the problem in one and several variables, its connection with the theory of conformal mappings and that of singular integrals, highlighting many open problems.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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