Bergman kernels for Paley-Wiener spaces and Nazarov's proof of the Bourgain-Milman theorem

Abstract

We give a general inequality for Bergman kernels of Bergman spaces defined by convex weights in $\C^n$. We also discuss how this can be used in Nazarov's proof of the Bourgain-Milman theorem, as a substitute for H\"ormander's estimates for the $\dbar$-equation.