Hardy Spaces and Canonical Kernels on Quadric CR Manifolds

Authors

Albert Boggess, Arizona State UniversityFollow
Jennifer Brooks, Brigham Young UniversityFollow
Andrew Raich, University of Arkansas, FayettevilleFollow

Document Type

Article

Publication Date

8-2024

Keywords

Quadric submanifolds; Higher codimension; Hardy spaces; Bergman projection; Bergman kernel; Szeg & ouml; projection; Szeg & ouml; kernel

Abstract

R functions on an embedded quadric M always extend holomorphically to M + iΓ_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 + iΓ_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.

Citation

Boggess, A., Brooks, J., & Raich, A. (2024). Hardy Spaces and Canonical Kernels on Quadric CR Manifolds. Journal of Geometric Analysis, 34 (8), 256. https://doi.org/10.1007/s12220-024-01708-4

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.