Pointwise estimates of weighted Bergman kernels in several complex variables

Original · EN

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.