Carleson measures on convex domains

TL;DR

This paper characterizes Carleson measures on bounded convex domains with smooth finite type boundaries, extending previous work on pseudoconvex domains, and provides examples with uniformly discrete sequences in the Kobayashi metric.

Contribution

It extends the characterization of Carleson measures to convex domains with smooth finite type boundaries and constructs examples with uniformly discrete sequences.

Findings

Characterization of Carleson measures on convex domains.

Examples of Carleson measures with uniformly discrete sequences.

Extension of prior results from pseudoconvex to convex domains.

Abstract

Following M.Abate and A.Saracco's work on strongly pseudoconvex domains in $\mathbb{C}^n$, we characterize Carleson measures of $A^2(D)$ in bounded convex domains with smooth boundary of finite type. We also give examples of Carleson measures with uniformly discrete (with respect to the Kobayashi distance) sequences.