学术报告：Oscillatory integral and Newton Polyhedron

 中科院数学与系统科学研究院

数学研究所

调和分析及其应用中心

学术报告会

报告人：Prof. Yan Duanyan （University of the The Chinese Academy of Sciences）

题  目：Oscillatory integral and Newton Polyhedron

时  间：12.05(星期五), 15:00--16:00

地  点：晨兴数学中心110室

摘 要： In this talk, we will introduce a class of oscillatory integral operators with the kernel being smooth function and compact support. Stein and Phong systematacially investigated those operators and obtained the sharp L² decay estimates. In fact, Stein’s results answered the important conjecture which was put by the distinguished mathematician Arnold. That is, the sharp decay estimate is determinated by the Newton polyhedron of the phase function of the oscillatory integral. Finally, we give the sharp L^p decay estimates of the oscillatory integral operators with homogeneous polynomial phases. As a consequence, we also give sharp L^p-boundedness of the generalized Fourier transform.