Boundary singularity of Poisson and harmonic Bergman kernels

2015/03/22 by Englis, Miroslav
#31B05 #46E22 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 32A36 #Secondary 32W25

paper · doi:10.48550/arxiv.1503.06440

Abstract

We give a complete description of the boundary behaviour of the Poisson kernel and the harmonic Bergman kernel of a bounded domain with smooth boundary, which in some sense is an analogue of the similar description for the usual Bergman kernel on a strictly pseudoconvex domain due to Fefferman. Our main tool is the Boutet de Monvel calculus of pseudodifferential boundary operators, and in fact we describe the boundary singularity of a general potential, trace or singular Green operator from that calculus.

Related

• Construction of boundary invariants and the logarithmic singularity of the Bergman kernel
• Toeplitz operators and weighted Bergman kernels
• Schrödinger operators with Leray-Hardy potential singular on the boundary
• The S.V.D. of the Poisson Kernel
• Asymptotic behavior of the Bergman kernel and associated invariants in weakly pseudoconvex domains