Title: Pointwise estimates of weighted Bergman kernels in several complex variables
Abstract: We prove new pointwise bounds for weighted Bergman kernels in ℂn, whenever a certain Laplacian acting on (0,1)-forms is coercive. 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 these Laplacians, inspired by the fact that these may be thought as a generalization of Schrödinger operators.
References:
1) Dall'Ara, G., Pointwise estimates of weighted Bergman kernels in several complex variables, Advances in Mathematics 285 (2015), 1706-1740.
2) Dall'Ara, G., Coercivity of weighted Kohn Laplacians: the case of model monomial weights in $\C^2$, to appear in Transactions of the American Mathematical Society.
Preprints are available here: http://arxiv.org/find/all/1/all:+dallara/0/1/0/all/0/1.