The Cauchy–Szegő projection for domains in Cn with minimal smoothness

Loredana Lanzani; Elias M. Stein

doi:10.1215/00127094-3714757

Abstract

We prove the $L^{p}(bD)$ -regularity of the Cauchy–Szegő projection (also known as the Szegő projection) for bounded domains $D\subset\mathbb{C}^{n}$ which are strongly pseudoconvex and whose boundary satisfies the minimal regularity condition of class $C^{2}$ .

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Loredana Lanzani. Elias M. Stein. "The Cauchy–Szegő projection for domains in $\mathbb{C}^{n}$ with minimal smoothness." Duke Math. J. 166 (1) 125 - 176, 15 January 2017. https://doi.org/10.1215/00127094-3714757

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Received: 12 June 2015; Revised: 18 February 2016; Published: 15 January 2017

First available in Project Euclid: 12 November 2016

zbMATH: 1367.32005

MathSciNet: MR3592690

Digital Object Identifier: 10.1215/00127094-3714757

Subjects:

Primary: 30E20 , 32A25 , 32A50 , 32A55

Secondary: 31A10 , 31B10 , 32A26 , 42B20 , 46E22 , 47B34

Keywords: $T(1)$ theorem , Cauchy integral , Cauchy–Szegő projection , Hardy space , Lebesgue space , Leray–Levi measure , minimal smoothness , pseudoconvex domain , space of homogeneous type

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