报告题目：Energy estimates for level sets of holomorphic functions and universal counterexamples to Calderón-Zygmund theory

报告人：潘一飞教授，美国印第安纳普渡大学韦恩堡分校

报告时间：2026年6月5日（周五）17:00-19:00

报告地点：20-308

报告摘要：The classical and fundamental Calderón-Zygmund theory fails at the end point 𝑝 = 1 for 𝐿^p spaces, which is a well-known textbook fact. In this talk I shall first show that, in fact, every holomorphic  function in ℂ" can generate a counterexample of the failure at 𝑝 = 1 via a double logarithmic transformation. The counterexamples would have singularity of any complex variety of codimension one. This is a joint work with Guokuan Shao, Jianfei Wang and Jujie Wu. Secondly, I will present the new results concerning the holomorphic sections of holomorphic line bundles over a compact Hermitian manifold with Energy estimates and global counterexamples of the Calderón-Zygmund theory in terms of global holomorphic sections. This is ongoing work with Guokuan Shao, Ziming Shi and Jujie Wu.

报告人简介：潘一飞，1990年毕业于密执安大学（University of Michigan），获博士学位。1990年至今执教于美国印第安纳普渡大学韦恩堡分校（Indiana university-Purdue university Fort Wayne），现为该校终身教授。研究方向包括多复变函数、偏微分方程、常微分方程等领域。在Duke Mathematical Journal、Mathematische Zeitschrift、Journal of Differential Equations、Communications in Partial Differential Equations、Annales de l'Institut Henri Poincaré.Analyse Non Linéaire、Michigan Mathematical Journal、Journal of Geometric Analysis等著名数学期刊上发表学术论文40余篇。

邀请人：刘洋