Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778536 | Advances in Mathematics | 2017 | 37 Pages |
Abstract
The one-dimensional oscillatory integral operator associated to a real analytic phase S is given byTλf(x)=â«âââeiλS(x,y)Ï(x,y)f(y)dy. In their fundamental work, Phong and Stein established sharp L2 estimates for Tλ. The goal of this paper is to extend their results to all endpoints. In particular, we obtain a complete characterization for the mapping properties for Tλ on Lp(R). More precisely, we show that âTλfâpâ²|λ|âαâfâp holds for some α>0 if and only if (1αp,1αpâ²) lies in the reduced Newton polygon of S.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Lechao Xiao,