Local smoothing and Hardy spaces for Fourier integral operators on manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866917577518743552 |
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| author | Liu, Naijia Rozendaal, Jan Song, Liang Yan, Lixin |
| author_facet | Liu, Naijia Rozendaal, Jan Song, Liang Yan, Lixin |
| contents | We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates for Fourier integral operators satisfying the cinematic curvature condition, and for wave equations on compact manifolds. The estimates are essentially sharp, for all $2<p<\infty$ and on each compact manifold. We also apply our local smoothing estimates to nonlinear wave equations with initial data outside of $L^{2}$-based Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10521 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Local smoothing and Hardy spaces for Fourier integral operators on manifolds Liu, Naijia Rozendaal, Jan Song, Liang Yan, Lixin Analysis of PDEs Classical Analysis and ODEs Primary 58J45. Secondary 35L05, 42B35, 35S30 We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates for Fourier integral operators satisfying the cinematic curvature condition, and for wave equations on compact manifolds. The estimates are essentially sharp, for all $2<p<\infty$ and on each compact manifold. We also apply our local smoothing estimates to nonlinear wave equations with initial data outside of $L^{2}$-based Sobolev spaces. |
| title | Local smoothing and Hardy spaces for Fourier integral operators on manifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs Primary 58J45. Secondary 35L05, 42B35, 35S30 |
| url | https://arxiv.org/abs/2211.10521 |