Duke Mathematical Journal

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

Loredana Lanzani and Elias M. Stein

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We prove the Lp(bD)-regularity of the Cauchy–Szegő projection (also known as the Szegő projection) for bounded domains DCn which are strongly pseudoconvex and whose boundary satisfies the minimal regularity condition of class C2.

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Duke Math. J., Volume 166, Number 1 (2017), 125-176.

Received: 12 June 2015
Revised: 18 February 2016
First available in Project Euclid: 12 November 2016

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Zentralblatt MATH identifier

Primary: 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx] 32A50: Harmonic analysis of several complex variables [See mainly 43-XX] 32A55: Singular integrals 32A25: Integral representations; canonical kernels (Szego, Bergman, etc.)
Secondary: 31A10: Integral representations, integral operators, integral equations methods 32A26: Integral representations, constructed kernels (e.g. Cauchy, Fantappiè- type kernels) 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 47B34: Kernel operators 31B10: Integral representations, integral operators, integral equations methods

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


Lanzani, Loredana; Stein, Elias M. The Cauchy–Szegő projection for domains in $\mathbb{C}^{n}$ with minimal smoothness. Duke Math. J. 166 (2017), no. 1, 125--176. doi:10.1215/00127094-3714757. https://projecteuclid.org/euclid.dmj/1478919691

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