Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

TL;DR

This paper investigates Carleson and sampling measures on Bernstein spaces defined on Siegel CR manifolds, establishing conditions for measures and sequences to be sampling or Carleson, advancing understanding of function spaces on these complex structures.

Contribution

It introduces and characterizes Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds, a novel setting in several complex variables.

Findings

Necessary and sufficient conditions for Carleson measures.

Necessary and sufficient conditions for sampling measures.

Sufficient conditions for sampling sequences.

Abstract

In this paper we introduce and study Carleson and sampling measures on Bernstein spaces on a class of quadratic CR manifold called Siegel CR manifolds. These are spaces of entire functions of exponential type whose restrictions to the given Siegel CR manifold are $L^p$-integrable with respect to a natural measure. For these spaces, we prove necessary and sufficients conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.