Hyponormal Toeplitz Operators on Weighted Bergman Spaces

关于Bergman核的局部化及其在Toeplitz理论中的应用

On the Localization of the Bergman Kernel and applications to Toeplitz theory

研究Bergman核在大线丛和Radon测度下的局部化现象，确认Zelditch猜想，并展示Toeplitz算子在组合下构成代数，其谱在Bernstein-Markov测度下均匀分布。

Boundedness and Compactness of Toeplitz operators with L^1 symbols on the Bergman space

We characterise the boundedness of a Toeplitz operator on the Bergman space with an L^1 symbol.We also prove that the compactness of a Toeplitz operator on the Bergman space with an L^1 symbol is completely determined by the boundary behaviour of itss Berezin transform. This result extends known results in the cases when the symbol is either a positive L^1 function, an L^\infty function or a general BMO^1 function.

Boundedness and Compactness of products of Toeplitz operators on the Bergman Space

In a celebrated conjecture D.Sarason stated a necessary and sufficient condition on the symbols f, g in the Bergman space, L^2_a(Δ) of the unit disk, Δ, for the products T_{f}T_{\bar g} of associated Toeplitz operators to be bounded (respectively compact) on L^2_a(Δ) . K. Stroethoff and D. Zheng proved that these conditions are necessary. We prove the sufficiency of these conditions, thus solvind Sarason's conjecture.

Bergman 空间上 Toeplitz 算子的加权理论

Weighted theory of Toeplitz operators on the Bergman space

本文研究 Bergman 空间上 Toeplitz 算子的加权紧性与有界性，刻画了紧算子并建立了有界性与端点弱型界。

Trace estimates of Toeplitz operators on Bergman spaces and applications to composition operators

Let $Ω$ be a subdomain of $\mathbb{C}$ and let $μ$ be a positive Borel measure on $Ω$. In this paper, we study the asymptotic behavior of the eigenvalues of compact Toeplitz operator $T_μ$ acting on Bergman spaces on $Ω$. Let $(λ_n(T_μ))$ be the decreasing sequence of the eigenvalues of $T_μ$ and let $ρ$ be an increasing function such that $ρ(n)/n^A$ is decreasing for some $A>0$. We give an explicit necessary and sufficient geometric condition on $μ$ in order to have $λ_n(T_μ)\asymp 1/ρ(n)$. As applications, we consider composition operators $C_φ$, acting on some standard analytic spaces on th…

Compact Operators on Vector-Valued Bergman Space via the Berezin Transform

In this paper, we characterise compactness of finite sums of finite products of Toeplitz operators acting on the $\mathbb{C}^{d}$-valued weighted Bergman Space, denoted $A_α^{p}(\mathbb{B}_{n},\mathbb{C}^{d})$. The main result shows that a finite sum of finite product of Toeplitz operators acting on $A_α^{p}(\mathbb{B}_n,\mathbb{C}_d)$ is compact if and only if its Berezin transform vanishes on the boundary of the ball.

$BMO^1_α$算子值符号在$\ell^2-$值Bergman空间上的Toeplitz算子分析

Analysis of Toeplitz Operators with $BMO^1_α$ operator-valued symbols on $\ell^2-$Valued Bergman Spaces

研究单位球上ℓ²值Bergman空间上具有BMO¹_α算子值符号的Toeplitz算子，通过有限维限制方法及充分条件刻画其紧性，并探讨逆蕴含问题。

Carleson embeddings and two operators on Bergman spaces of tube domains over symmetric cones

We prove Carleson embeddings for Bergman spaces of tube domains over symmetric cones, we apply them to characterize symbols of bounded Cesàro-type operators from weighted Bergman spaces to weighted Besov spaces. We also obtain Schatten class criteria of Toeplitz operators and Cesàro-type operators on weighted Hilbert-Bergman spaces.

Sarason Conjecture on the Bergman space

We provide a counterexample to the Sarason Conjecture for the Bergman space and present a characterisation of bounded Toeplitz products on the Bergman space in terms of test functions by means of a dyadic model approach. We also present some results about two-weighted estimates for the Bergman projection. Finally, we introduce the class $B_{\infty}$ and give sharp estimates for the one-weighted Bergman projection.

The Essential Norm of Operators on the Bergman Space of Vector--Valued Functions on the Unit Ball

Let $A_α^{p}(\mathbb{B}^n;\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ of functions taking values in $\mathbb{C}^d$. For $1<p<\infty$ let $\mathcal{T}_{p,α}$ be the algebra generated by finite sums of finite products of Toeplitz operators with bounded matrix--valued symbols (this is called the Toeplitz algebra in the case $d=1$). We show that every $S\in \mathcal{T}_{p,α}$ can be approximated by localized operators. This will be used to obtain several equivalent expressions for the essential norm of operators in $\mathcal{T}_{p,α}$. We then use…