报告人：付祥迪（复旦大学）

时间：2023年11月8日 9:30-

地点：理科楼LA103；腾讯会议ID：724-757-138

摘要：The classical Hardy-Littlewood maximal function of $f\in L^1(\mathbb R^d)$ is defined as $$M_df(x):= \sup_{r>0} \frac{1}{Q(x,r)}\int_{Q(x,r)} |f(t)|dt,$$where $Q(x,r)$ is the closed $\ell^\infty$-ball of radius $r$ and center $x$. It is well known that the weak type (1,1) estimation holds, namely, there exists a constant $c_d$, such that $$|\{x: M_df(x)>\alpha\}| \leq \frac{c_d}{\alpha} \|f\|_1, \,\,\,\alpha>0,\,\,f\in L^1(\mathbb R^d).$$ A basic question, raised by E. M. Stein and J.-O. Str\"omberg, is that whether the (best) constants $c_d$ are uniformly bounded. Recently, J. M. Aldaz [Ann. of Math. 2011] proved that $c_d$ growth to infinity with the dimension. In this talk, we will report his proof in detail and then discuss some related questions in the function theory of infinite many variables.

报告人简介：付祥迪，复旦大学博士生。主要研究方向为泛函分析，其相关结果发表在Sci. China Math.、Studia Math等期刊。

具体见附件

邀请人：秦越石、王奕、王子鹏、晏福刚、赵显锋

欢迎广大师生积极参与！