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arXiv · 1503.06440

Boundary singularity of Poisson and harmonic Bergman kernels

Miroslav Englis
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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.

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Miroslav Englis. 2015-03-22. Boundary singularity of Poisson and harmonic Bergman kernels. https://arxiv.org/abs/1503.06440

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