The Bergman projection in $L^p$ for domains with minimal smoothness

Loredana Lanzani; Elias M. Stein

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arXiv · 1201.4148

The Bergman projection in $L^p$ for domains with minimal smoothness

Loredana Lanzani·Elias M. Stein

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Abstract

Let $D\subset\mathbb C^n$ be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove $L^p(D)$-regularity for the Bergman projection $B$, and for the operator $|B|$ whose kernel is the absolute value of the Bergman kernel with $p$ in the range $(1,+\infty)$. As an application, we show that the space of holomorphic functions in a neighborhood of $\bar{D}$ is dense in $\vartheta L^p (D)$.

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BibTeX RIS

Loredana Lanzani, Elias M. Stein. 2012-10-04. The Bergman projection in $L^p$ for domains with minimal smoothness. https://arxiv.org/abs/1201.4148

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