Boundary singularity of Poisson and harmonic Bergman kernels
Classical Analysis and ODEs
2015-03-24 v1 Analysis of PDEs
Complex Variables
Functional Analysis
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.
Cite
@article{arxiv.1503.06440,
title = {Boundary singularity of Poisson and harmonic Bergman kernels},
author = {Miroslav Englis},
journal= {arXiv preprint arXiv:1503.06440},
year = {2015}
}
Comments
submitted to J. Math. Anal. Appl. on December 30 2011