2006/09/28 by Miroslav Engliš, Miroslav Englis, Englis, Miroslav
Mathematics · #32A25 #32A36 #32W25 #47B35 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.AP #math.CV #math.FA #msc:32A25 #msc:32A36 #msc:32W25 #msc:47B35
paper · pdf · doi:10.48550/arxiv.math/0609800
35 pages, no figures
arxiv created 2006/09/28 · openalex publication_date 2006/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman kernel. Finally, we also exhibit a holomorphic continuation of the kernels with respect to the Sobolev parameter to the entire complex plane. Our main tool are the generalized Toeplitz operators of Boutet de Monvel and Guillemin.