7 problems

Let $p>1$, let $\alpha>1$, let $0<s<1$, let $\mu$ be a positive Borel measure on the open unit disc $\mathbb D$, and let $F(p,p\alpha-2,s)$ and ${\mathfrak T}_{s,p}^{\infty}(\mu)$…

Let $p>1$, let $0<s<1$, let $\mu$ be a positive Borel measure on the open unit disc $\mathbb D$, and let $F(p,p-2,s)$ and ${\mathcal T}_{s,p}^p(\mu)$ denote the function and tent s…

Let $0<s<1$ and let $\mu$ be a positive Borel measure on the open unit disc $\mathbb D$. The spaces ${\mathcal Q}_s$ and ${\mathcal T}_{s,2}^2(\mu)$ are linked by the identity map…

Let $H^p$ denote the Hardy space on the unit disk, let $\mu$ be a positive Borel measure on $[0,1)$, and let $\mathcal{DH}_\mu$ denote the derivative-Hilbert operator associated wi…

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 $G$ be an open subset, with components whose harmonic measures are considered. A positive measure $\mu$ on $G$ is a Carleson measure when it satisfies the relevant Carleson emb…

Let $G$ be a domain conformally equivalent to a circular domain $W$, and let $\phi:G\to W$ be a conformal map. A positive measure on $G$ is a Carleson measure if it satisfies the C…