$L^p$-boundedness of multi-parameter Fourier integral operators
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916412158640128 |
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| author | Cheng, Jinhua |
| author_facet | Cheng, Jinhua |
| contents | We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter Hörmander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots + n_d$. Our investigation focuses on cases where the phase function $Φ(x,ξ)$ can be decomposed into a sum of individual components $Φ_i(x_i,ξ_i)$, with each component satisfying a non-degeneracy condition. We extend the Seeger-Sogge-Stein theorem under the condition that the dimension $ n_i \ge 2$ for each
$1\le i \le d$. As a corollary, we obtain the boundedness of multi-parameter Fourier integral operators on local Hardy spaces, Lipschitz spaces, and Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14178 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L^p$-boundedness of multi-parameter Fourier integral operators Cheng, Jinhua Classical Analysis and ODEs We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter Hörmander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots + n_d$. Our investigation focuses on cases where the phase function $Φ(x,ξ)$ can be decomposed into a sum of individual components $Φ_i(x_i,ξ_i)$, with each component satisfying a non-degeneracy condition. We extend the Seeger-Sogge-Stein theorem under the condition that the dimension $ n_i \ge 2$ for each $1\le i \le d$. As a corollary, we obtain the boundedness of multi-parameter Fourier integral operators on local Hardy spaces, Lipschitz spaces, and Sobolev spaces. |
| title | $L^p$-boundedness of multi-parameter Fourier integral operators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2307.14178 |