意大利赌场线路

极大函数谱乘子的有界性

2024.09.27

投稿:龚惠英部门:理学院浏览次数:

活动信息

报告题目 (Title):极大函数谱乘子的有界性

报告人 (Speaker):陈鹏 教授(中山大学)

报告时间 (Time):2024年9月29日(周日)10:30

报告地点 (Place):校本部 GJ403

邀请人(Inviter):赵发友

主办部门:理学院 数学系

报告摘要:Let $(X,d,\mu)$ be a metric space with doubling measure and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ whose heat kernel satisfies Gaussian upper bound. Given Hormander type spectral multipliers $m_i,1\leq i\leq N$ with uniform estimates, we prove an optimal $\sqrt{\log(1+N)}$ bound in $L^p$ for the maximal function $\sup_{1\leq i\leq N}|m_i(L)f|$ by making use of Doob transform and some techniques as in Grafakos-Honzik-Seeger to use the ${\rm exp}(L^2)$ estimate by Chang-Wilson-Wolff. Based on this, we establish sufficient conditions on the bounded Borel function $m$ such that the maximal function $ M_{m,L}$ given by $M_{m,L}f(x) = \sup_{t>0} |m(tL)f(x)|$ is bounded on $L^p$. The applications include Scattering operators, Schrodinger operators with inverse square potential, Dirichlet Laplacian with Dirichlet boundary, Bessel operators and Laplace-Beltrami operators.

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