Pau–Zhao's Carleson embedding conjecture for $F(p,p-2,s)$

Let $p>1$, let $0<s<1$, let $\mu$ be a positive Borel measure on the open unit disc $\mathbb D$, and let $F(p,p-2,s)$ and ${\mathcal T}_{s,p}^p(\mu)$ denote the function and tent spaces in the source. Pau–Zhao's conjecture. The identity map

$$id:F(p,p-2,s)\mapsto {\mathcal T}_{s,p}^p(\mu)$$

is bounded if and only if $\mu$ is an $s$-Carleson measure. The paper proves a near-endpoint version with $t<s$; it also explains that an endpoint result requires modifying the Carleson-measure definition by incorporating a logarithmic factor, so the stated conjecture remains open in the supplied text.