5 problems

Let $v$ be an admissible weight, let $X$ be either $\operatorname{BMOA}_v$ or $\operatorname{VMOA}_v$, and assume $X\not\subset H^\infty$. Let $\delta_z$ denote evaluation at $z$,…

Let $v$ be an admissible weight, and let $\phi\colon\mathbb D\to\mathbb D$ be an analytic polynomial symbol. The polynomial-symbol conjecture. The composition operator … is bounded…

Let $v$ be a weight, let $\phi\colon\mathbb D\to\mathbb D$ be an analytic symbol, and let $\psi$ be an analytic function. The boundedness-assumption conjecture. The assumption in T…

Let $\mathbb D$ denote the unit disk, let $v\colon\mathbb D\to(0,\infty)$ be an increasing radial weight that is not admissible, let $\hat\phi\in\operatorname{Aut}(\mathbb D)$, and…

Let $v$ be a weight on the unit disk and let $p$ be the parameter appearing in Proposition 1. Assume that the function $x\mapsto v(1-x)x^{\frac{1}{p}-\epsilon}$ is almost increasin…