题目: Multilinear Weighted Convolution of L^2 Functions, and Application to Nonlinear Dispersive Equations

报告时间： 6月18日下午: 2:00--5:00 (星期五)

报告时间： 6月23日下午: 2:00--5:00 (星期三)

报告时间： 6月25日下午: 2:00--5:00 (星期五)

报告时间： 6月30日下午: 2:00--5:00 (星期三)

报告人：　中物院研究生部, 郑继强

文章摘要：The X_{s,b} spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel’s theorem and duality, these estimates reduce to estimating a weighted convolution integral in terms of the L^2 norms of the component functions. In this paper we systematically study weighted convolution estimates on L^2. As a consequence we obtain sharp bilinear estimates for the KdV, wave, and Schrodinger X_{s,b} spaces.