Tent spaces at endpoints (Q1697689)

\textit{R. R. Coifman} et al. [J. Funct. Anal. 62, 304--335 (1985; Zbl 0569.42016)] developed a theory of tent spaces \(T^p_q(\mathbb{R}^{n+1}_{+}),\;1< p,q < \infty\). The authors investigate tent spaces at endpoints. The authors show that the predual of tent space \(T^1_{\infty}(\mathbb{R}^{n+1}_{+})\) is the vanishing Carleson measure space on \(\mathbb{R}^{n+1}_{+}\). They also give the characterization of \(T^{\infty}_q(\mathbb{R}^{n+1}_{+})\) via the boundedness of the Poisson type integral. As application they give the boundedness and compactness on \(L^q(\mathbb{R}^n)\) of the paraproduct associated with the tent space \(T^{\infty}_q(\mathbb{R}^{n+1}_{+})\).