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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.
演讲者介绍
Hajer Ben Amor is a PhD candidate in Mathematics at the Faculty of Sciences of Gabès, University of Gabès, Tunisia, under the supervision of Prof. Noureddine Ghiloufi. Her research focuses on modified Bergman spaces, reproducing kernels, and harmonic analysis on complex domains.
She is visiting BIMSA with support from the ICMRA Visiting Scholars Program.
She is visiting BIMSA with support from the ICMRA Visiting Scholars Program.