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Spring 2012 The Bergman projection in $L^{p}$ for domains with minimal smoothness
Loredana Lanzani, Elias M. Stein
Illinois J. Math. 56(1): 127-154 (Spring 2012). DOI: 10.1215/ijm/1380287464

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

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Loredana Lanzani. Elias M. Stein. "The Bergman projection in $L^{p}$ for domains with minimal smoothness." Illinois J. Math. 56 (1) 127 - 154, Spring 2012. https://doi.org/10.1215/ijm/1380287464

Information

Published: Spring 2012
First available in Project Euclid: 27 September 2013

zbMATH: 1282.32001
MathSciNet: MR3117022
Digital Object Identifier: 10.1215/ijm/1380287464

Subjects:
Primary: 31B, 32A, 42B

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

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Vol.56 • No. 1 • Spring 2012
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