Projections onto $L^p$-Bergman spaces of Reinhardt Domains

Abstract

For $1<p<\infty$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the kernel is shown to be absolutely bounded projection on the $L^p$-Bergman space on a class of domains where the $L^p$-boundedness of the Bergman projection fails for certain $p\ne 2$. As an application, we identify the duals of these $L^p$-Bergman spaces with weighted Bergman spaces.

arXiv commentFinal verson with typos fixed. To appear in Advances in Mathematics

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Cited by in corpus (1)

• Extensions of Daubechies' theorem: Reinhardt domains, Hagedorn wavepackets and mixed-state localization operators