Pointwise estimates of weighted Bergman kernels in several complex variables

2015/02/03 by Gian Maria Dall'Ara, Dall'Ara, Gian Maria
Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV

paper · pdf · doi:10.48550/arxiv.1502.00865

26 pages

arxiv created 2015/02/03 · arxiv updated 2015/02/04

Abstract

We prove new pointwise bounds for weighted Bergman kernels in ℂⁿ, whenever a coercivity condition is satisfied by the associated weighted Kohn Laplacian on (0,1)-forms. Our results extend the ones obtained in ℂ by Christ. Our main idea is to develop a version of Agmon theory (originally introduced to deal with Schrödinger operators) for weighted Kohn Laplacians on (0,1)-forms, inspired by the fact that these are unitarily equivalent to certain generalized Schrödinger operators.

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