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