Bergman projection on the symmetrized bidisk

Lipschitz type characterizations for Bergman Spaces

We obtain new characterizations for Bergman spaces with standard weights in terms of Lipschitz type conditions in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we prove optimal embedding theorems when an analytic function on the unit disk is symmetrically lifted to the bidisk.

$L^p$正则性研究：伯格曼投影在对称化多边形域上的表现

$L^p$ regularity of the Bergman projection on the symmetrized polydisc

该研究探讨了伯格曼投影在对称化多边形域上的$L^p$正则性，通过分解和等价算子分析，确定了$p$的范围对$P$有界性的决定性影响。

Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc

A natural class of weighted Bergman spaces on the symmetrized polydisc is isometrically embedded as a subspace in the corresponding weighted Bergman space on the polydisc. We find an orthonormal basis for this subspace. It enables us to compute the kernel function for the weighted Bergman spaces on the symmetrized polydisc using the explicit nature of our embedding. This family of kernel functions include the Szegö and the Bergman kernel on the symmetrized polydisc.

Bergman metric on the symmetrized bidisc and its consequences

On the symmetrized bidisc G2 with the Bergman metric, the holomorphic sectional curvature is negatively pinched and the holomorphic bisectional curvature is not. The consequences in invariant metrics are provided.

Poletsky-Stessin 加权 Bergman 空间中的循环性

Cyclicity in Poletsky-Stessin Weighted Bergman Spaces

本文研究单位球、双圆盘和复椭球上 Poletsky-Stessin 加权 Bergman 空间中多项式的循环性，通过扩展参数范围构造类 Dirichlet 型空间，揭示与已有研究的差异并提出若干公开问题。

$L^p$ regularity of the Bergman Projection on domains covered by the polydisk

If a bounded domain can be covered by the polydisk through a rational proper holomorphic map, then the Bergman projection is $L^p$-bounded for $p$ in a certain range depending on the ramified rational covering. This result can be applied to the symmetrized polydisk and to the Hartogs triangle with exponent $γ$.

Weighted Bergman spaces and the integral means spectrum of conformal mappings

We study the so-called integral means spectrum for univalent functions on the unit disk. Using an inequality of Prawitz (generalizing the classical area theorem of Gronwall), we find -- by applying a Moebius mapping to lift the result to the bidisk -- that it is possible to obtain rather strong estimates from above on the integral means spectrum.

商域上加权Bergman空间上的Toeplitz算子

Toeplitz operators on the weighted Bergman spaces of quotient domains

利用有限伪反射群的不变理论与表示理论，建立商域上加权Bergman空间Toeplitz算子的恒等式，并应用于广义零积问题与交换对刻画，在对称化多圆盘等特殊商域获得精细结果。

Norm expansion along a zero variety in ${\mathbb C}^d$

The reproducing kernel function of a weighted Bergman space over domains in ${\mathbb C}^d$ is known explicitly in only a small number of instances. Here, we introduce a process of orthogonal norm expansion along a subvariety of codimension 1, which also leads to a series expansion of the reproducing kernel in terms of reproducing kernels defined on the subvariety. The problem of finding the reproducing kernel is thus reduced to the same kind of problem when one of the two entries is on the subvariety. A complete expansion of the reproducing kernel may be achieved in this manner. We carry this…