Tent Carleson measures for Hardy spaces

TL;DR

This paper characterizes measures on the unit ball that ensure bounded embeddings from Hardy spaces to tent-type spaces, providing a comprehensive understanding of Carleson measures in this context.

Contribution

It offers a complete characterization of Carleson measures for Hardy spaces into tent-type spaces across all parameter ranges.

Findings

Identifies necessary and sufficient conditions for measures to be Carleson measures.

Provides a unified framework for understanding embeddings of Hardy spaces.

Extends previous results to all parameter values.

Abstract

We completely characterize those positive Borel measures $\mu$ on the unit ball $\mathbb{B}_ n$ such that the Carleson embedding from Hardy spaces $H^p$ into the tent-type spaces $T^q_ s(\mu)$ is bounded, for all possible values of $0<p,q,s<\infty$.