报告人：吴清艳（临沂大学）

时 间：2023年6月15日上午8:30

地 点：腾讯会议560-348-509（无密码）

内容摘要:

Products of Siegel upper half spaces are Siegel domains, whose Silov boundaries have the structure of products $\mathscr H_1\times\mathscr H_2$ of Heisenberg groups. By the reproducing formula of bi-parameter heat kernel associated to sub-Laplacians, we show that a function in holomorphic Hardy space $H^1$ on such a domain has boundary value belonging to bi-parameter Hardy space $H^1(\mathscr H_1\times \mathscr H_2)$. With the help of atomic decomposition of $H^1(\mathscr H_1\times \mathscr H_2)$ and bi-parameter harmonic analysis, we show that the Cauchy-Szeg\H o projection is a bounded operator from $H^1 (\mathscr H_1\times \mathscr H_2)$ to holomorphic Hardy space $H^1$, and any holomorphic $H^1$ function can be decomposed as a sum of holomorphic atoms. Bi-parameter atoms on $\mathscr H_1\times\mathscr H_2$ are more complicated than $1$-parameter ones, and so are holomorphic atoms.

个人简介：

吴清艳，临沂大学数学与统计学院教授，博士生导师。主要从事多复变函数论和调和分析的研究，特别是这两个方向的相互交叉与应用。在J. Funct. Anal., Indiana Univ. Math. J., Proc. Amer. Math. Soc.等数学杂志上发表学术论文30余篇，先后主持国家自然科学基金3项、山东省自然科学基金3项。

联系人：杨东勇