Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 2

Special issue in honor of Joseph J. Kohn on the occasion of his 90th birthday

Guest Editors: J.E. Fornaess, Stanislaw Janeczko, Duong H. Phong, and Stephen S.T. Yau

Bergman kernels for Paley–Wiener spaces and Nazarov’s proof of the Bourgain–Milman theorem

Pages: 395 – 409

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n2.a2


Bo Berndtsson (Department of Mathematics, Chalmers University of Technology and the University of Göteborg, Sweden)


We give a general inequality for Bergman kernels of Bergman spaces defined by certain convex weights in $\mathbb{C}^n$. We also discuss how this can be used in Nazarov’s proof of the Bourgain–Milman theorem, as a substitute for Hörmander’s estimates for the $\overline{\partial}$-equation.

Received 20 October 2020

Accepted 13 December 2020

Published 13 May 2022