Carleson measures for Hardy-Sobolev spaces in the Siegel upper half-space

TL;DR

This paper characterizes Carleson measures for Hardy-Sobolev spaces in the Siegel upper half-space using capacitary methods, addressing a question posed by previous researchers and advancing understanding of function space measures.

Contribution

It provides a capacitary characterization of Carleson measures for Hardy-Sobolev spaces in the Siegel upper half-space, partially answering an open question.

Findings

Capacitary conditions characterize Carleson measures in this setting

The results extend previous work on Hardy-Sobolev spaces

Addresses an open problem posed by Arcozzi et al.

Abstract

We give a capacitary type characterization of Carleson measures for a class of Hardy-Sobolev spaces (also known as weighted Dirichlet spaces) on the Siegel upper half-space, introduced by Arcozzi et al. This answers in part a question raised by the same authors.