Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains

TL;DR

This paper characterizes Carleson measures in strongly pseudoconvex domains using the Bergman kernel, extends known results from the unit ball, and explores the behavior of uniformly discrete sequences with respect to the Kobayashi distance.

Contribution

It generalizes Carleson measure characterizations and the properties of uniformly discrete sequences from the unit ball to strongly pseudoconvex domains in several complex variables.

Findings

Characterization of Carleson measures via Bergman kernel in strongly pseudoconvex domains

Uniformly discrete sequences are examples of Carleson measures in these domains

Computed the boundary escape speed of uniformly discrete sequences in strongly pseudoconvex domains

Abstract

We characterize using the Bergman kernel Carleson measures of Bergman spaces in strongly pseudoconvex bounded domains in several complex variables, generalizing to this setting theorems proved by Duren and Weir for the unit ball. We also show that uniformly discrete (with respect to the Kobayashi distance) sequences give examples of Carleson measures, and we compute the speed of escape to the boundary of uniformly discrete sequences in strongly pseudoconvex domains, generalizing results obtained in the unit ball by Jevti\'c, Massaneda and Thomas, by Duren and Weir, and by MacCluer.