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Algebra i Analiz, 2014, Volume 26, Issue 1, Pages 196–269 (Mi aa1374)  

This article is cited in 7 scientific papers (total in 7 papers)

Research Papers

Extremal bases, geometrically separated domains and applications

Ph. Charpentier, Y. Dupain

Université Bordeaux 1, Institut de Mathématiques, 351, cours de la Libération, 33405 Talence, France
Full-text PDF (708 kB) Citations (7)
References:
Abstract: The notion of an extremal basis of tangent vector fields is introduced for a boundary point of finite type of a pseudo-convex domain in $\mathbb C^n$, $n\geq3$. By using this notion, the class of geometrically separated domains at a boundary point is defined and a description of their complex geometry is presented. Examples of such domains are given, for instance, by locally lineally convex domains, domains with locally diagonalizable Levi form at a point, or by domains for which the Levi form has comparable eigenvalues near a point. Moreover, it is shown that geometrically separated domains can be localized. An example of a not geometrically separated domain is presented. Next, the so-called “adapted plurisubharmonic functions” are defined and sufficient conditions, related to extremal bases, for their existence are given. Then, for these domains, when such functions exist, global and local sharp estimates are proved for the Bergman and Szegö projections. As an application, a result by C. Fefferman, J. J. Kohn, and M. Machedon for the local Hölder estimate of the Szegö projection is refined, by removing the arbitrarily small loss in the Hölder index and giving a stronger nonisotropic estimate.
Keywords: finite type, extremal basis, complex geometry, adapted plurisubharmonic function, Bergman and Szegö projections.
Received: 24.09.2012
English version:
St. Petersburg Mathematical Journal, 2015, Volume 26, Issue 1, Pages 139–191
DOI: https://doi.org/10.1090/S1061-0022-2014-01335-0
Bibliographic databases:
Document Type: Article
Language: English
Citation: Ph. Charpentier, Y. Dupain, “Extremal bases, geometrically separated domains and applications”, Algebra i Analiz, 26:1 (2014), 196–269; St. Petersburg Math. J., 26:1 (2015), 139–191
Citation in format AMSBIB
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\jour Algebra i Analiz
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\pages 139--191
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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