Brevig–Ortega-Cerdà–Seip–Zhao conjecture on contractive Hardy–Dirichlet inclusions

Let $p>2$, let $\mathbb{D}$ be the unit disk, and let $f$ be analytic in $\mathbb{D}$. Denote by $\|f\|_{H^p}$ the Hardy-space norm and by $\|f\|_{D_{p/2}}$ the norm of the corresponding Dirichlet space. Brevig–Ortega-Cerdà–Seip–Zhao conjecture. The inequality

$$\| f \|_{H^p} \leq \| f \|_{D_{\frac{p}{2}}}$$

holds for all such $f$. This conjecture concerns contractive inclusions between Hardy and Dirichlet spaces; the supplied source does not state whether it has been resolved.