5 problems

Let $B_p$ be the analytic Besov space with $p>2$, and let $C_{\varphi}$ denote the composition operator induced by an analytic self-map $\varphi$ of the disk, defined by…

Asymptotic limit conjecture. For any $\alpha>-1$,

For $\alpha\geq 0$, let … In particular, $H^{\infty}_0$ is the Banach space of bounded analytic functions, and $T_g$ denotes the Volterra type operator with symbol $g$. Anderson–Jo…

Constancy conjecture. Then $g$ is constant. The source presents this as a proposed extension of the assertion that non-constant outer solutions do not occur in the corresponding cl…

Let $\gamma>0$. For $f\in {\mathcal A}^1_{\gamma}$, write $f=f_\mu=\exp(-h_\mu)$ for its uniquely determined premeasure $\mu\in P^+_{\kappa_\gamma}(\mathbb T)$, and let…