调和分析研讨课
课程编码：180080070101D4001Z
英文名称：Seminar on Harmonic Analysis
课时：20
学分：1.00
课程属性：研讨课
主讲教师：Quoc-Hung Nguyen (阮国兴)
教学目的要求
"The purpose of this course is for students to learn Littlewood–Paley theory,
Besov Spaces and Commutator Estimates and Kato-ponce inequalities, Integral of Oscillating Functions, Strichartz Estimates and Applications to nonlinear dispersive Equations."
预修课程
无
大纲内容
第一章 Basic Analysis; Littlewood–Paley Theory 10.0学时 Quoc-Hung Nguyen (阮国兴)
第1节 Sobolev, Hardy and Interpolation Spaces
第2节 Littlewood–Paley decomposition
第3节 Besov Spaces
第4节 Paradifferential Calculus
第5节 Commutator Estimates and Kato-ponce inequalities
第二章 Strichartz Estimates and Applications
to Semilinear Dispersive Equations 10.0学时 Quoc-Hung Nguyen (阮国兴)
第1节 Integral of Oscillating Functions and their application
第2节 Bilinear Methods
第3节 Strichartz Estimates for the Wave Equation
第4节 Applications to nonlinear dispersive Equations
参考书
1、
Fourier Analysis and Nonlinear Partial Differential Equation
H. Bahouri, J.Y. Chemin, R. Danchin,
2013年2月
Springer
课程教师信息
略