报告题目：Weighted Estimates for Singular Integrals and One-Sided Maximal Operators

报告人：Sheldy Javier Ombrosi，Universidad Nacional del Sur and CONICET

报告时间：2026年10月9日-10月11日（周五-周日）8:30-12:00

报告地点：20-404

报告摘要：This three-day course will focus on two topics in harmonic analysis:the solution of the $C_p$ conjecture and the behavior of one-sidedmaximal operators in higher dimensions. The first two lectures will present a complete proof of the $C_p$conjecture, based on joint work with A.~Lerner and F.~Nazarov.We will show that the condition $w\in C_p$ is sufficient for the estimate

\[\int_{\mathbb{R}^n}|Tf|^p w\lesssim\int_{\mathbb{R}^n}(Mf)^p w,\qquad 1<p<\infty,< font="">\]

for Calder\'on--Zygmund operators admitting standard sparse domination,where $M$ denotes the Hardy--Littlewood maximal operator.The proof will be developed in detail, explaining the roles of sparsedomination, dyadic tails, Bellman function techniques, and randomdyadic lattices. The third lecture will provide an overview of one-sided maximaloperators in higher dimensions, highlighting the difficulties thatarise beyond the one-dimensional setting. We will then discuss jointwork with F.~Nazarov establishing the failure of an endpoint estimateand a positive result under an additional bump condition.

报告人简介：Sheldy Javier Ombrosi，阿根廷国立南方大学数学系教授、博士生导师。他同时担任阿根廷国家科学与技术研究委员会(CONICET)的Investigador Principal研究员、Bihia Blanca数学研究所所长、阿根廷数学联合会(UMA)第二副主席，以及《Revista de la Unión Matemática Argentina》主编。主要从事调和分析，尤其是奇异积分算子的加权理论的研究，在Muckenhoupt猜想、多线性权理论、奇异积分算子的最优端点加权估计、单边权理论等问题上取得了一系列重要成果。在Adv. Math., Math. Ann., Anal. PDE, TAMS等高水平期刊上发表学术论文40余篇。

邀请人：李康伟