2 problems

Let $D$ denote the Dirichlet space, let $L^2_a$ denote the Bergman space, and let $M_\phi$ be multiplication by a finite Blaschke product $\phi$ of order $n$ on $L^2_a$. A reducing…

Gu's conjecture. The following are equivalent: $A_B^\theta$ has a reducing subspace such that the restriction has one-dimensional defects; and $\theta(z)=b(z)u(z^N)$ for some inner…