Exact $L^2$ convergence through the wavelet and tent space characterizations of $h^p(\mathbb{R}^n)$, $0<p\le 1$

We extend the wavelet and tent space characterization of $h^1(\mathbb{R}^n)$ to $0<p\le 1$ via a local dyadic tent space $t_p$, and derive the unconditional $L^2$-convergence of the resulting atomic decomposition, with an exact error identity refining Ding, Jiang and Zhu (2019).