强伪凸域上的Carleson测度与一致离散序列

Skew Carleson measures in strongly pseudoconvex domains

Given a bounded strongly pseudoconvex domain $D$ in $\mathbb{C}^n$ with smooth boundary, we give a characterization through products of functions in weighted Bergman spaces of $(λ,γ)$-skew Carleson measures on $D$, with $λ>0$ and $γ>1-\frac{1}{n+1}$.

强伪凸域上的Toeplitz算子与Carleson测度

Toeplitz operators and Carleson measures in strongly pseudoconvex domains

研究了n个复变数中有界强伪凸区域D上与有限正Borel测度相关联的Toeplitz算子的映射性质.特别地，我们给出了保证伴随Toeplitz算子将Bergman空间A^p（D）映射到A^r（D）且r>p的严格测度条件，推广了Cuckovic和McNeal的结果，使其更为精确.要做到这一点，我们给出了一个几何特征的Carleson措施和消失Carleson措施的加权Bergman空间的内在小林几何的域，推广到这一设置的结果Kaptanoglu单位球。

Toeplitz Operators and Skew Carleson measures for weighted Bergman spaces on strongly pseudoconvex domains

In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted Bergman kernel of weight $β$ and integrating against a measure $μ$ maps continuously (when $β$ is large enough) a weighted Bergman space $A^{p_1}_{α_1}(D)$ into a weighted Bergman space $A^{p_2}_{α_2}(D)$ if and only if $μ$ is a $(λ,γ)$-skew Carleson measure, where $λ=1+\frac{1}{p_1}-\frac{1}{p_2}$ and $γ=\frac{1}λ\left(β+\frac{α_1}{p_1}-\frac{α_2}{p_2}\right)$.…

Dyadic Carleson embedding and sparse domination of weighted composition operators on strictly pseudoconvex domains

In this paper, we study the behavior of the weighted composition operators acting on Bergman spaces defined on strictly pseudoconvex domains via the sparse domination technique from harmonic analysis. As a byproduct, we also prove a weighted type estimate for the weighted composition operators which is adapted to Sawyer-testing conditions. Our results extend the work by the first author, Li, Shi and Wick under a much more general setting.

Carleson measures on convex domains

Following M.Abate and A.Saracco's work on strongly pseudoconvex domains in $\mathbb{C}^n$, we characterize Carleson measures of $A^2(D)$ in bounded convex domains with smooth boundary of finite type. We also give examples of Carleson measures with uniformly discrete (with respect to the Kobayashi distance) sequences.

A remark on Carleson measures of domains in $\mathbb{C}^{n}$

We provide characterizations of Carleson measures on a certain class of bounded pseudoconvex domains. An example of a vanishing Carleson measure whose Berezin transform does not vanish on the boundary is given in the class of the Hartogs triangles $$\mathbb{H}_{k}:=\left\{ \left(z_{1},z_{2}\right)\in\mathbb{C}^{2}:\left|z_{1}\right|^{k}<\left|z_{2}\right|<1\right\},\;k\in\mathbb{Z}^{+}.$$