Pointwise estimates of weighted Bergman kernels in several complex variables

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 by Christ in [5].Our main idea is to develop a version of Agmon theory (originally introduced in [1] 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.