Department of Mathematics, Macquarie University
题目: Boundedness of certain singular integrals with non-smooth kernel on non-doubling manifold with ends
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。