Tent Carleson measures and superposition operators on Hardy type tent spaces

TL;DR

This paper characterizes measures for bounded Carleson embeddings between Hardy type tent spaces and determines conditions for inclusion and superposition operators, advancing understanding of function space mappings in complex analysis.

Contribution

It provides a complete characterization of measures for bounded embeddings and describes when superposition operators between Hardy type tent spaces are bounded.

Findings

Characterization of measures for bounded Carleson embeddings

Conditions for inclusion between Hardy type tent spaces

Complete description of superposition operators between these spaces

Abstract

In this paper, we completely characterize the positive Borel measures $\mu$ on the unit ball $\mathbb{B}_n$ of $\mathbb{C}^n$ such that the Carleson embedding from holomorphic Hardy type tent spaces $\mathcal{HT}^p_{q,\alpha}$ into the tent spaces $T^t_s(\mu)$ is bounded for all $0<p,q,s,t<\infty$ and $\alpha>-n-1$. As an application, we determine the indices $0<p,q,s,t<\infty$ and $\alpha,\beta>-n-1$ such that the inclusion $\mathcal{HT}^p_{q,\alpha}\subset\mathcal{HT}^t_{s,\beta}$ holds, which allows us to completely characterize the nonlinear superposition operators between Hardy type tent spaces.