Abstract
We prove a variable coefficient version of the square function estimate of Guth–Wang–Zhang. By a classical argument of Mockenhaupt–Seeger–Sogge, it implies the full range of sharp local smoothing estimates for (Formula presented.) -dimensional Fourier integral operators satisfying the cinematic curvature condition. In particular, the local smoothing conjecture for wave equations on compact Riemannian surfaces is settled.
| Original language | English |
|---|---|
| Pages (from-to) | 1923-1960 |
| Number of pages | 38 |
| Journal | Proceedings of the London Mathematical Society |
| Volume | 126 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2023 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
Funding
This project was supported by the National key R&D program of China No. 2022YFA1005700 and 2022YFA1007200. C. Gao was supported by Chinese Postdoc Foundation Grant No. 8206300279. B. Liu was supported by SUSTech start‐up counterpart Y01286235. C. Miao was partially supported by NSF China grant No.11831004. Y. Xi was partially supported by NSF China grant No. 12171424 and the Fundamental Research Funds for the Central Universities 2021QNA3001. The authors would like to thank Ruixiang Zhang for suggesting this problem. The authors would like to thank Larry Guth and Hong Wang for some helpful comments. The authors would like to thank the anonymous referees for their valuable comments and suggestions, which have greatly improved the presentation of this paper.
| Funders | Funder number |
|---|---|
| Chinese Postdoc Foundation | 8206300279, Y01286235 |
| National Natural Science Foundation of China | 12171424, 11831004 |
| National Key Research and Development Program of China | 2022YFA1007200, 2022YFA1005700 |
| Fundamental Research Funds for the Central Universities | 2021QNA3001 |