The Littlewood-Paley type g-function, the Lusin type s-function, and their applications

报告人：陈少林（衡阳师范学院）

时  间：2026年5月27日16:00

地  点：海韵园行政楼C503

内容摘要:

The purpose of this talk is twofold. First, we investigate several properties of the Littlewood-Paley type g-function and the Lusin type s-function associated with the invariant Laplacian (or Laplace-Beltrami) operator. Our work extends and refines some of the main results established by Kwon [Trans. Am. Math. Soc. 355: 1269-1294, 2003]. Second, we employ these g- and  s-functions to study the Riesz conjugate functions theorem. As a consequence, we generalize and improve  the main results of Liu and Zhu [Adv. Math. 434: 109321, 2023]. Additionally, our results provide a partial answer to an open problem posed by Astala and Koskela [Pure Appl. Math. Q. 7: 19-50, 2011].

个人简介：

陈少林，博士，教授。长期从事几何函数理论及其应用研究，已解决该领域公开问题3个。曾先后访问印度马德拉斯理工学院、拉马努金数学研究所，以及芬兰赫尔辛基大学、阿尔托大学和图尔库大学。在《Sci. China, Math.》《Adv. Math.》《J. Funct. Anal.》《Indiana Univ. Math. J.》《Math. Z.》《J. Anal. Math.》《Israel J. Math.》等国内外数学期刊上发表学术论文50余篇。曾获湖南省优秀博士学位论文奖、湖南省自然科学奖二等奖和三等奖各1项。主持多项科研项目，其中包括国家自然科学基金项目4项、国家科技部项目1项、中国博士后科学基金面上项目（一等资助）1项等。

联系人：钟春平