Hardy Spaces and Canonical Kernels on Quadric CR Manifolds

CR functions on an embedded quadric M always extend holomorphically to M + i Γ M where Γ M is the closure of the convex hull of the image of the Levi form. When Γ M is a closed polygonal cone, we show that the Bergman kernel on the interior of M + i Γ M is a derivative of the Szegö kernel. Moreover,...

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Bibliographic Details
Published in:The Journal of geometric analysis 2024, Vol.34 (8), p.256, Article 256
Main Authors: Boggess, Albert, Brooks, Jennifer, Raich, Andrew
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Convexity
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
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Summary:CR functions on an embedded quadric M always extend holomorphically to M + i Γ M where Γ M is the closure of the convex hull of the image of the Levi form. When Γ M is a closed polygonal cone, we show that the Bergman kernel on the interior of M + i Γ M is a derivative of the Szegö kernel. Moreover, we develop the L p Hardy space theory which turns out to be particularly robust. We provide examples that show that it is unclear how to formulate a corresponding relationship between the Bergman and Szegö kernels on a wider class of quadrics.
ISSN:1050-6926
1559-002X
1559-002X
DOI:10.1007/s12220-024-01708-4