3 problems

Let $\mathbb D$ be the unit disk, let $\varphi$ be an analytic self-mapping of $\mathbb D$, and let $C_{\varphi}f=f\circ\varphi$ be bounded on the Dirichlet space…

The Carleson embedding conjecture. This condition is necessary and sufficient for Carleson measures on $\mathcal{D}$. Combining the known result of Arcozzi, Rochberg, and Sawyer wi…

Discrete capacitary conjecture. The discrete capacitary condition together with the separation condition (Sep) is necessary and sufficient for $S$ to be onto interpolating for the…