Square function inequality for oscillatory integral operators satisfying homogeneous Carleson-Sjölin type conditions
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| Format: | Preprint |
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2019
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| _version_ | 1866913322635362304 |
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| author | Gao, Chuanwei Miao, Changxing Yang, Jianwei-Urbain |
| author_facet | Gao, Chuanwei Miao, Changxing Yang, Jianwei-Urbain |
| contents | In this paper, we establish an improved variable coefficient version of square function inequality, by which the local smoothing estimate $L^p_α\rightarrow L^p$ for the Fourier integral operators satisfying cinematic curvature condition is further improved. In particular, we establish almost sharp results for $2<p\leq 3$ and push forward the estimate for the critical point $p=4$. As a consequence, the local smoothing estimate for the wave equation on the manifold is refined. We generalize the results in \cite{LeVa12, Le18P} to its variable coefficient counterpart. The main ingredients in the argument includes multilinear oscillatory integral estimate \cite{BCT06} and decoupling inequality \cite{BelHicSog18P}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1901_01489 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Square function inequality for oscillatory integral operators satisfying homogeneous Carleson-Sjölin type conditions Gao, Chuanwei Miao, Changxing Yang, Jianwei-Urbain Analysis of PDEs 35S30, 35L15 In this paper, we establish an improved variable coefficient version of square function inequality, by which the local smoothing estimate $L^p_α\rightarrow L^p$ for the Fourier integral operators satisfying cinematic curvature condition is further improved. In particular, we establish almost sharp results for $2<p\leq 3$ and push forward the estimate for the critical point $p=4$. As a consequence, the local smoothing estimate for the wave equation on the manifold is refined. We generalize the results in \cite{LeVa12, Le18P} to its variable coefficient counterpart. The main ingredients in the argument includes multilinear oscillatory integral estimate \cite{BCT06} and decoupling inequality \cite{BelHicSog18P}. |
| title | Square function inequality for oscillatory integral operators satisfying homogeneous Carleson-Sjölin type conditions |
| topic | Analysis of PDEs 35S30, 35L15 |
| url | https://arxiv.org/abs/1901.01489 |