The weak (1,1) boundedness of Fourier integral operators with complex phases
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866912908245467136 |
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| author | Cardona, Duván Ruzhansky, Michael |
| author_facet | Cardona, Duván Ruzhansky, Michael |
| contents | Let $T$ be a Fourier integral operator of order $-(n-1)/2$ associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, Sogge, and Stein proved in the 90's, gives the boundedness of $T$ from the Hardy space $H^1$ into $L^1.$ Additionally, it was shown by T. Tao the weak (1,1) type of $T$. In this work, we establish the weak (1,1) boundedness of a Fourier integral operator $T$ of order $-(n-1)/2$ when it has associated a canonical relation parametrised by a complex phase function. This result in the complex-valued setting, cannot be derived from its counterpart in the real-valued case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The weak (1,1) boundedness of Fourier integral operators with complex phases Cardona, Duván Ruzhansky, Michael Analysis of PDEs Functional Analysis Let $T$ be a Fourier integral operator of order $-(n-1)/2$ associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, Sogge, and Stein proved in the 90's, gives the boundedness of $T$ from the Hardy space $H^1$ into $L^1.$ Additionally, it was shown by T. Tao the weak (1,1) type of $T$. In this work, we establish the weak (1,1) boundedness of a Fourier integral operator $T$ of order $-(n-1)/2$ when it has associated a canonical relation parametrised by a complex phase function. This result in the complex-valued setting, cannot be derived from its counterpart in the real-valued case. |
| title | The weak (1,1) boundedness of Fourier integral operators with complex phases |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2402.09054 |