2 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…

Let $D_1$ denote the Dirichlet space, and let $f\in D_1$. A function is cyclic in $D_1$ if the polynomials multiplied by it are dense in $D_1$. A function $f\in D_1$ is outer if it…