Illinois Journal of Mathematics

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

Loredana Lanzani and Elias M. Stein

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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 $\overline{D}$ is dense in $\vartheta L^{p}(D)$.

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Illinois J. Math., Volume 56, Number 1 (2012), 127-154.

First available in Project Euclid: 27 September 2013

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Zentralblatt MATH identifier

Primary: 32A 42B 31B


Lanzani, Loredana; Stein, Elias M. The Bergman projection in $L^{p}$ for domains with minimal smoothness. Illinois J. Math. 56 (2012), no. 1, 127--154. doi:10.1215/ijm/1380287464.

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