5 problems

Let $\mathbb{B}_n$ denote the unit ball, and let $A^p_\alpha$ be the weighted Bergman space on $\mathbb{B}_n$, where $0<p<\infty$ and $\alpha$ is real. Zhu's reciprocal conjecture.…

Lieb–Solovej conjecture. If $p>2$, then

Let $H^2$ be the Hardy space on the unit disk, let $A^p_\beta$ denote the standard weighted Bergman space with exponent $p$ and weight parameter $\beta$, and let the Szegő kernel b…

Holomorphic stability conjecture. For any boundary-accessable measure $\mu$ on $\mathbb{D}$, the pair $(B^2(\mathbb{D},\mu),h^1(\mathbb{D}))$ is holomorphically stable if and only…

Let $A^2_1$ be the weighted Bergman space of holomorphic functions on the unit disk with norm … For $H\in A^2_1$, write … the smallest closed subspace of $A^2_1$ containing $H$ and…