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ICMRA 系列讲座
ICMRA 系列讲座
Weighted Bergman Spaces on the Unit Ball of $\mathbb{C}^n$: Reproducing Kernels and Applications
Weighted Bergman Spaces on the Unit Ball of $\mathbb{C}^n$: Reproducing Kernels and Applications
演讲者
Hajer Ben Amor
时间
2026年06月30日 14:00 至 15:00
地点
A3-4-101
线上
Zoom 204 323 0165
(BIMSA)
摘要
We introduce new spaces $A^p_{a,b}(\mathbb{B}^n)$ of holomorphic functions on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$, generalizing the classical Bergman spaces. We present properties of these spaces and determine the reproducing kernel in the case $p=2$, then study the boundedness of Bergman projections. Using the Berezin transform, a Bergman--Poincaré type metric is introduced, with applications to BMO functions. These results extend several classical properties of Bergman theory to weighted settings.
As a perspective for future research, I aim to investigate the zero distribution of hypergeometric functions and hypergeometric polynomials. The goal is to describe their asymptotic localization using analytic and potential-theoretic techniques, and to explore possible connections with reproducing kernel structures in weighted Bergman-type spaces.
As a perspective for future research, I aim to investigate the zero distribution of hypergeometric functions and hypergeometric polynomials. The goal is to describe their asymptotic localization using analytic and potential-theoretic techniques, and to explore possible connections with reproducing kernel structures in weighted Bergman-type spaces.