Related papers: Essential Commutants on Strongly Pseudo-convex Dom…

One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb{D}$ in the complex place $\mathbb{C}$ is to completely describe the commutant of a given Toeplitz operator, that is, the set of all…

The well-known Axler-Zheng theorem characterizes compactness of finite sums of finite products of Toeplitz operators on the unit disk in terms of the Berezin transform of these operators. Subsequently this theorem was generalized to other…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^2$ with Lipschitz boundary or a bounded convex domain in $\mathbb{C}^n$ and $\phi\in C(\overline{\Omega})$ such that $H_{\phi}$ is compact on $A^2(\Omega)$. Then $\phi\circ f$ is…

Let $\Omega\subset \mathbb{C}^n$ be a smooth bounded pseudoconvex domain and $A^2 (\Omega)$ denote its Bergman space. Let $P:L^2(\Omega)\longrightarrow A^2(\Omega)$ be the Bergman projection. For a measurable $\varphi:\Omega\longrightarrow…

Let $\lambda$ be a complex number in the closed unit disc $\overline{\Bbb D}$, and $\cal H$ be a separable Hilbert space with the orthonormal basis, say, ${\cal E}=\{e_n:n=0,1,2,\cdots\}$. A bounded operator $T$ on $\cal H$ is called a {\em…

In this paper, we provide a complete characterization of bounded Toeplitz operators $T_f$ on the harmonic Bergman space of the unit disk, where the symbol $f$ has a polar decomposition truncated above, that commute with $T_{z+\bar{g}}$, for…

Given an n-tuple of multiplication operators on the Bergman space of a bounded pseudoconvex domain in C^n, we study the algebra of their commutants. In particular, we give a geometric description of the maximal C*-subalgebra of this…

We study mapping properties of Toeplitz operators associated to a finite positive Borel measure on a bounded strongly pseudoconvex domain D in n complex variables. In particular, we give sharp conditions on the measure ensuring that the…

We characterize the commutant of the analytic Toeplitz operators modulo operators of Schatten-p-class on suitable multivariable domains. We show that a result of J. Xia on compact perturbations of Toeplitz operators on the unit disc remains…

We consider Volterra-type integration operators $T_g$ between Bergman spaces induced by weights $\omega$ satisfying a doubling property. We derive estimates for the operator norms, essential and weak essential norms of $T_g: A_\omega^p \to…

We study positive Toeplitz operators on the Bergman spaces having the fast decreasing weight functions in a certain class. We give the characterizations for the boundedness and compactness of Toeplitz operators in terms of their Berezin…

We make a progress towards describing the semi-commutants of Toeplitz operators on Fock-Sobolev spaces of nonnegative orders. We generalize the results in \cite{Bauer1,Qin}. For the certain symbol spaces, we obtain two Toeplitz operators…

In a celebrated conjecture D.Sarason stated a necessary and sufficient condition on the symbols f, g in the Bergman space, L^2_a(\Delta) of the unit disk, \Delta, for the products T_{f}T_{\bar g} of associated Toeplitz operators to be…

As a class of compact operators on the $\ell^2-$valued Bergman space $A^2_\alpha (\mathbb B_n, \ell^2)$ on the unit ball $\mathbb B_n,$ we study Toeplitz operators with $BMO^1_\alpha (\mathbb B_n, \mathcal L(\ell^2))$ operator-valued…

In this paper we characterize the compact operators on $A^p_\alpha(\mathbb{B}_n)$ when $1<p<\infty$ and $\alpha>-1$. The main result shows that an operator on $A^p_\alpha(\mathbb{B}_n)$ is compact if and only if it belongs to the Toeplitz…

We study spectra of Toeplitz operators $T_a $ with periodic symbols in Bergman spaces $A^2(\Pi)$ on unbounded periodic planar domains $\Pi$, which are defined as the union of infinitely many copies of the translated, bounded periodic cell…

Let $\Omega\subset\mathbb{C}^m$ be a bounded pseudoconvex domain with smooth boundary. For each $k\in\mathbb{N}$, we give a sufficient condition to estimate the $\bar\partial$-Neumann operator in the Sobolev space $W^k(\Omega)$. The key…

In this paper, we completely characterize when two dual truncated Toeplitz operators are essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact. Our main idea is to study dual truncated…

Necessary and sufficient conditions for positive Toeplitz operators on the Bergman space of a minimal bounded homogeneous domain to be bounded or compact are described in terms of the Berezin transform, the averaging function and the…

Let $\alpha\in (0, 1]$, $\beta\in [0, n)$ and $T_{\Omega,\beta}$ be a singular or fractional integral operator with homogeneous kernel $\Omega$. In this article, a CMO type space ${\rm CMO}_\alpha(\mathbb R^n)$ is introduced and studied. In…