Boundary singularity of Poisson and harmonic Bergman kernels

0446809 - MÚ 2016 RIV US eng J - Journal Article
Engliš, Miroslav
Boundary singularity of Poisson and harmonic Bergman kernels.
Journal of Mathematical Analysis and Applications. Roč. 429, č. 1 (2015), s. 233-272. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA AV ČR IAA100190802
Institutional support: RVO:67985840
Keywords : harmonic Bergman kernel * Poisson kernel * pseudodifferential boundary operators
Subject RIV: BA - General Mathematics
Impact factor: 1.014, year: 2015
http://www.sciencedirect.com/science/article/pii/S0022247X15003170

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.
Permanent Link: http://hdl.handle.net/11104/0248777