Tent Carleson measures and superposition operators on Hardy type tent spaces

Abstract

In this paper, we completely characterize the positive Borel measures $\hat{I}¼$ on the unit ball ${\mathbb{B}}_n$ of ${\mathbb{C}}^n$ such that the Carleson embedding from holomorphic Hardy type tent spaces ${\mathcal{H}\mathcal{T}}_{q,\hat{I}\pm }^p$ into the tent spaces $T_s^t(\hat{I}¼)$ is bounded for all $0<p,q,s,t<\infty$ and $\hat{I}\pm >-n-1$. As an application, we determine the indices $0<p,q,s,t<\infty$ and $\hat{I}\pm ,{\hat{I}}^2>-n-1$ such that the inclusion ${\mathcal{H}\mathcal{T}}_{q,\hat{I}\pm }^p\subset {\mathcal{H}\mathcal{T}}_{s,{\hat{I}}^2}^t$ holds, which allows us to completely characterize the nonlinear superposition operators between Hardy type tent spaces.