Oscillatory integral and Newton polyhedron
主 题: Oscillatory integral and Newton polyhedron
报告人: 燕敦验教授 (中国科学院)
时 间: 2014-10-17 15:00-16:00
地 点: 理科一号楼1114（数学所活动）
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 $L^2$ decay estimates. In fact, Stein’s results answered the important conjecture which was put by 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.