A sharp Schrodinger maximal estimate in R2

• 成果类型: Article
• 署名作者: Du, Xiumin; Guth, Larry; Li, Xiaochun
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.186.2.5
• 发表日期: 2017
• 页码: 607-640
• 关键词: pointwise convergence; equation

摘要

We show that lim(t -> 0) e(it Delta) f(x) = f(x) almost every where for all f is an element of H-s (R-2) provided that s > 1/3. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.