Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on Complex Balls

TL;DR

This paper characterizes Carleson measures for the Drury-Arveson Hardy space and related spaces, providing geometric conditions and sharp estimates that enhance understanding of these function spaces in several complex variables.

Contribution

It introduces the 'split tree condition' as a geometric criterion for Carleson measures, advancing the analysis of Hilbert spaces of analytic functions.

Findings

Characterization of Carleson measures via the split tree condition

Sharp estimates for Drury's generalization of Von Neumann's inequality

Connection between geometric conditions and function space properties

Abstract

We characterize the Carleson measures for the Drury-Arveson Hardy space and other Hilbert spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The characterization is in terms of a geometric condition, the "split tree condition", which reflects the nonisotropic geometry underlying the Drury-Arveson Hardy space.