51. A note on the refined Strichartz estimates and maximal extension operator
- Author
-
Shukun Wu
- Subjects
Class (set theory) ,Pure mathematics ,General Mathematics ,Bilinear interpolation ,02 engineering and technology ,01 natural sciences ,symbols.namesake ,Operator (computer programming) ,Mathematics - Analysis of PDEs ,Principal curvature ,0202 electrical engineering, electronic engineering, information engineering ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,0101 mathematics ,Mathematics ,Partial differential equation ,Applied Mathematics ,010102 general mathematics ,020206 networking & telecommunications ,Decoupling (cosmology) ,Extension (predicate logic) ,Fourier analysis ,Mathematics - Classical Analysis and ODEs ,symbols ,Analysis ,Analysis of PDEs (math.AP) - Abstract
There are two parts for this paper. In the first part, we extend some results in a recent paper by Du, Guth, Li and Zhang to a more general class of phase functions. The main methods are Bourgain-Demeter's $l^2$ decoupling theorem and induction on scales. In the second part, we prove some positive results for the maximal extension operator for hypersurfaces with positive principal curvatures. The main methods are sharp $L^2$ estimates by Du and Zhang, and the bilinear method by Wolff and Tao., 24 pages, revised version incorporating referees' suggestions
- Published
- 2020