Mizohata-Takeuchi inequalities for orthonormal systems
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912424122122240 |
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| author | Bennett, Jonathan Bez, Neal Gutierrez, Susana Nakamura, Shohei Oliveira, Itamar |
| author_facet | Bennett, Jonathan Bez, Neal Gutierrez, Susana Nakamura, Shohei Oliveira, Itamar |
| contents | We establish some weighted $L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process we develop a direct approach to such inequalities based on generalised Wigner distributions, complementing the Schatten duality approach that is prevalent in the wider context of estimates for such orthonormal systems. Our results are set within a broader family of tentatively suggested ($L^p$) inequalities of Mizohata--Takeuchi type. For $p$ an even integer we see that such weighted inequalities may be recast as questions of co-positivity of tensor forms, and for $p\leq 1$ we provide some evidence that they may hold in reverse provided the orthonormal sequence is complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mizohata-Takeuchi inequalities for orthonormal systems Bennett, Jonathan Bez, Neal Gutierrez, Susana Nakamura, Shohei Oliveira, Itamar Classical Analysis and ODEs We establish some weighted $L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process we develop a direct approach to such inequalities based on generalised Wigner distributions, complementing the Schatten duality approach that is prevalent in the wider context of estimates for such orthonormal systems. Our results are set within a broader family of tentatively suggested ($L^p$) inequalities of Mizohata--Takeuchi type. For $p$ an even integer we see that such weighted inequalities may be recast as questions of co-positivity of tensor forms, and for $p\leq 1$ we provide some evidence that they may hold in reverse provided the orthonormal sequence is complete. |
| title | Mizohata-Takeuchi inequalities for orthonormal systems |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2506.03783 |