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We provide a characterization of the commutant of analytic Toeplitz operators $T_B$ induced by finite Blachke products $B$ acting on weighted Bergman spaces which, as a particular instance, yields the case $B(z)=z^n$ on the Bergman space solved recently by by Abkar, Cao and Zhu. Moreover, it extends previous results by Cowen and Wahl in this context and applies to other Banach spaces of analytic functions such as Hardy spaces $H^p$ for $1<p<infty$. Finally, we apply this approach to study reducing subspaces of $T_{B}$ in the classical Bergman space. As a particular instance, we provide a direct proof of a theorem of Hu, Sun, Xu and Yu which states that every analytic Toeplitz operator $T_B$ induced by a finite Blachke product on the Bergman space is reducible and the restriction of $T_B$ on a reducing subspace is unitarily equivalent to the Bergman shift.
Let $mathcal{D}$ be the class of radial weights on the unit disk which satisfy both forward and reverse doubling conditions. Let $g$ be an analytic function on the unit disk $mathbb{D}$. We characterize bounded and compact Volterra type integration o
This paper is devoted to the study of reducing subspaces for multiplication operator $M_phi$ on the Dirichlet space with symbol of finite Blaschke product. The reducing subspaces of $M_phi$ on the Dirichlet space and Bergman space are related. Our st
We completely characterize the simultaneous membership in the Schatten ideals $S_ p$, $0<p<infty$ of the Hankel operators $H_ f$ and $H_{bar{f}}$ on the Bergman space, in terms of the behaviour of a local mean oscillation function, proving a conjecture of Kehe Zhu from 1991.
A full description of the membership in the Schatten ideal $S_ p(A^2_{omega})$ for $0<p<infty$ of the Toeplitz operator acting on large weighted Bergman spaces is obtained.
In this paper, we study the reducing subspaces for the multiplication operator by a finite Blaschke product $phi$ on the Dirichlet space $D$. We prove that any two distinct nontrivial minimal reducing subspaces of $M_phi$ are orthogonal. When the ord