Commuting Dual Toeplitz Operators on the Polydisk

On the polydisk, the commutativity of dual Toeplitz operators is studied. We obtain characterizations of commuting dual Toeplitz operators, essentially commuting dual Toeplitz operators and essentially semi-commuting dual Toeplitz operators.     

Composition Operators on Weighted Bergman–Orlicz Spaces on the Ball

We give embedding theorems for weighted Bergman–Orlicz spaces on the ball and then apply our results to the study of the boundedness and the compactness of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted Bergman–Orlicz spaces, different from H ^∞, on which every composition operator is bounded.     

Sarason's Toeplitz Product Problem on the Fock–Sobolev Space

The Sarason's Toeplitz product problem asks when the Toeplitz product operator Tu T_v,with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the Fock–Sobolev space and have a complete solution that u = e~q, v = Ce~(-q),where q is a linear complex polynomial and C is a nonzero constant.     

Closures of Hardy and Hardy–Sobolev Spaces in the Bloch Type Space on the Unit Ball

For \(0<\alpha <\infty \), \(0<p<\infty \) and \(0<s<\infty \), we characterize the closures in the \(\alpha \)-Bloch norm of \(\alpha \)-Bloch functions that are in a Hardy space \(H^p\) and in a Hardy–Sobolev space \(H^p_s\) on the unit ball of \(\mathbb {C}^n\).     

k-order Slant Toeplitz Operators on the Bergman Space

In this paper κ-order slant Toeplitz operator on the Bergman space is defined. Some properties like spectrum, commuting are discussed.     

Bounded Hankel Products on the Weighted Bergman Space

1 Introduetion The Bergman spaeeA足15 the spaee of analytie funetions on a plane domain D whieh are square integrable with resPeet to the measure dA。(:)=(a 1)(1一l:I“)“己且(之)，where dA denotes the normalized Lebesgue area measure on D.The reProdueing kernel in A蕊15 given妙K1a)(:) 1 (1一场:)2 a之，叨任D. If(·，·)。denotes the inner produet in LZ(D，dA。)，then (。，K;a))。=人(二) h oA蕊，二。D. The orthogonal projeetion凡of LZ(D，dA。)ontoA且15 given by‘Pa。)(?卜(。，玲，)一…     

The Generalized Schwarz–Pick Estimates of Arbitrary Order on the Unit Polydisk

Let Ω be a homogeneous circular convex domain (a bounded symmetric domain) in ${\mathbb{C}^N}$ containing the origin. The generalization of the Schwarz–Pick estimates of partial derivatives of arbitrary order are established for holomorphic mappings from the unit polydisk D _n to Ω associated with the Carathéodory metric. The metric enables us to obtain some known results from a unified perspective and also leads some new results. In particular, our results are valid for the Cartan domains. When Ω = B _N , the Schwarz–Pick estimates of high order reduces to that of Liu and Chen.     

Commutants of Toeplitz operators with radial symbols on the Fock–Sobolev space

In the setting of the Fock space over the complex plane, Bauer and Lee have recently characterized commutants of Toeplitz operators with radial symbols, under the assumption that symbols have at most polynomial growth at infinity. Their characterization states: If one of the symbols of two commuting Toeplitz operators is nonconstant and radial, then the other must be also radial. We extend this result to the Fock–Sobolev spaces.     

On the Representation of Linear Continuous Functionals in Spaces of Analytic Functions of the Hardy–Sobolev Type in a Polydisk

We describe dual spaces of classes of the Hardy–Sobolev type of functions holomorphic in a polydisk for 0 < p 1 and q (0, ) and for p (1, ) and q = 1.     

Products of Toeplitz Operators on the Polydisk

This paper studies products of Toeplitz operators on the Hardy space of the polydisk. We show that T _f T _g = 0 if and only if T _f T _g is a finite rank if and only if T _f or T _g is zero. The product T _f T _g is still a Toeplitz operator if and only if there is a h $ \in $ L $ \infty $ (T ⁿ ) such that T _f T _g - T _h is a finite rank operator. We also show that there are no compact simi-commutators with symbols pluriharmonic on the polydisk. Submitted: October 5, 2000     

Finite Sums of Toeplitz Products on the Polydisk

On the Bergman space of the unit polydisk, we study a class of operators which contains sums of finitely many Toeplitz products with pluriharmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. As one of applications we show that sums of a certain number, depending on and increasing with the dimension, of semicommutators of Toeplitz operators with pluriharmonic symbols cannot be compact without being the zero operator.     

Toeplitz and Hankel Products on Bergman Spaces of the Unit Ball

The authors give some new necessary conditions for the boundedness of Toeplitz products Tf^aTg^a on the weighted Bergman space Aa^2 of the unit ball, where f and g are analytic on the unit ball. Hankel products HfH9^＋ on the weighted Bergman space of the unit ball are studied, and the results analogous to those Stroethoff and Zheng obtained in the setting of unit disk are proved.     

Invertible Toeplitz Operators Products on the Bergman Space of the Polydisk

We prove a reverse Hlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk.Next,we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products Tf Tg are bounded invertible Toeplitz operators.     

多元盘Bergman空间上可逆的Toeplitz算子乘积

We prove a reverse Hlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk.Next,we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products Tf Tg are bounded invertible Toeplitz operators.     

Toeplitz Corona Theorems for the Polydisk and the Unit Ball

The main purpose of this paper is to extend and refine some work of Agler–McCarthy and Amar concerning the Corona problem for the polydisk and the unit ball in \mathbbCⁿ\mathbb{C}^n.     

Radial Operators on the Weighted Bergman Spaces over the Polydisk

In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the(m, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its(0, λ)-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its(m, λ)-Berezin transform is a separately radial function.     

Bounded and Invertible Toeplitz Products on Vector Weighted Bergman Spaces of the Unit Polydisc

We characterize bounded and invertible Toeplitz products on vector weighted Bergman spaces of the unit polydisc. For our purpose, we will need the notion of Békollé–Bonami weights in several parameters.     

多圆盘上的对偶Toeplitz代数

本文证明了对偶Toeplitz代数${\cal I}(C(\overline{D^n}))$的半换位理想是紧算子全体,并研究了其代数结构,得到了对偶Toeplitz算子的一些谱性质.     

多圆盘Bergman空间上Toeplitz算子的乘积和交换性

该文给出了多圆盘Bergman空间上两个带有某种符号的Toeplitz算子的乘积等于另一个Toeplitz算子的充分必要条件,并且给出了乘积算子所带符号的公式.接下来,相应的研究了它的交换性.这些研究结果都是根据符号函数的Mellin变换.