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学术报告: Boundedness of certain singular integrals with non-smooth kernel on non-doubling manifold with ends

发布时间:2019年01月08日 浏览次数:发布者:mathky

报告人:李冀 副教授 

              Department of Mathematics, Macquarie University

题目: Boundedness of certain singular integrals with non-smooth kernel on non-doubling manifold with ends

时间:2019年01月09日下午14:30

地点:海韵实验楼108

摘要: Let Δ be the Laplace-Beltrami operator acting on a non-doubling manifold with two ends Rm#Rn with m > n ≥3. Let ht(x; y) be the kernels of the semigroup e-tΔgenerated by Δ. We say that a non-negative self-adjoint operator L on L2( Rm#Rn ) has a heat kernel with upper bound of Gaussian type if the kernel ht(x; y) of the semigroup e-tL satisfies ht(x; y)≤Chαt(x; y) for some constants C and α. This class of operators includes the Schrödinger operator L = Δ + V where V is an arbitrary non-negative potential. We then obtain upper bounds of the Poisson semigroup kernel of L together with its time derivatives and use them to show the weak type (1; 1) estimate for the holomorphic functional calculus M(L1/2) where M(z) is a function of Laplace transform type. Our result covers the purely imaginary powers Lis; s∈R, as a special case and serves as a model case for weak type (1; 1) estimates of singular integrals with non-smooth kernels on non-doubling spaces. The results we provide here are based on recent result with The Anh Bui, Xuan Thinh Duong and Brett D. Wick.

报告人简介:李冀副教授的研究方向为调和分析, 主要研究多参数的调和分析, 度量空间上的函数空间以及与算子相关的函数空间及其应用. 目前共发表学术论文44篇,其研究工作先后发表在 Appl. Comput. Harmon. Anal., Trans. Amer. Math. Soc., Anal. & PDE, J. Math. Pures Appl.和 J. Funct. Anal.等国际著名数学杂志上。

联系人:杨东勇副教授

 

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