Function spaces for decoupling
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916026025771008 |
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| author | Hassell, Andrew Portal, Pierre Rozendaal, Jan Yung, Po-Lam |
| author_facet | Hassell, Andrew Portal, Pierre Rozendaal, Jan Yung, Po-Lam |
| contents | We introduce new function spaces $\mathcal{L}_{W,s}^{q,p}(\mathbb{R}^{n})$ that yield a natural reformulation of the $\ell^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half-wave propagators, but not under all Fourier integral operators unless $p=q$, in which case they coincide with the Hardy spaces for Fourier integral operators. We use these spaces to obtain improvements of the classical fractional integration theorem and local smoothing estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Function spaces for decoupling Hassell, Andrew Portal, Pierre Rozendaal, Jan Yung, Po-Lam Analysis of PDEs Classical Analysis and ODEs Primary 42B35. Secondary 42B37, 35L05, 35S30 We introduce new function spaces $\mathcal{L}_{W,s}^{q,p}(\mathbb{R}^{n})$ that yield a natural reformulation of the $\ell^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half-wave propagators, but not under all Fourier integral operators unless $p=q$, in which case they coincide with the Hardy spaces for Fourier integral operators. We use these spaces to obtain improvements of the classical fractional integration theorem and local smoothing estimates. |
| title | Function spaces for decoupling |
| topic | Analysis of PDEs Classical Analysis and ODEs Primary 42B35. Secondary 42B37, 35L05, 35S30 |
| url | https://arxiv.org/abs/2302.12701 |