A class of multi-parameter Fourier integral operators: endpoint Hardy space bounds
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929510080839680 |
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| author | Cheng, Jinhua |
| author_facet | Cheng, Jinhua |
| contents | In this paper we study a class of Fourier integral operators, whose symbols lie in the multi-parameter Hörmander class $S^{\vec m}( \mathbb{R}^\vn)$, where ~$\vec m=(m_1,m_2,\dots,m_d)$ is the order. We show that if in addition the phase function $Φ(x,ξ)$ can be written as $Φ(x,ξ)=\sum_{i=1}^dΦ_i(x_i,ξ_i)$, and each $Φ_i(x_i,ξ_i)$ satisfies the non-degeneracy condition, then such Fourier integral operators with order ~$\vec m=(-(n_1-1)/2, -(n_2-1)/2,\dots, -(n_d-1)/2)$ are actually bounded from rectangular Hardy space $H_{rect}^1(\mathbb{R}^\vn)$ to $L^1( \mathbb{R}^n )$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A class of multi-parameter Fourier integral operators: endpoint Hardy space bounds Cheng, Jinhua Classical Analysis and ODEs Analysis of PDEs In this paper we study a class of Fourier integral operators, whose symbols lie in the multi-parameter Hörmander class $S^{\vec m}( \mathbb{R}^\vn)$, where ~$\vec m=(m_1,m_2,\dots,m_d)$ is the order. We show that if in addition the phase function $Φ(x,ξ)$ can be written as $Φ(x,ξ)=\sum_{i=1}^dΦ_i(x_i,ξ_i)$, and each $Φ_i(x_i,ξ_i)$ satisfies the non-degeneracy condition, then such Fourier integral operators with order ~$\vec m=(-(n_1-1)/2, -(n_2-1)/2,\dots, -(n_d-1)/2)$ are actually bounded from rectangular Hardy space $H_{rect}^1(\mathbb{R}^\vn)$ to $L^1( \mathbb{R}^n )$. |
| title | A class of multi-parameter Fourier integral operators: endpoint Hardy space bounds |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2401.13482 |