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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2305.00125 |
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| _version_ | 1866909468994830336 |
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| author | Johnsrude, Ben |
| author_facet | Johnsrude, Ben |
| contents | We note that the subpolynomial factor for the $\ell^qL^p$ small cap decoupling constants for the truncated parabola $\mathbb{P}^1=\{(t,t^2):|t|\leq 1\}$ may be controlled by a suitable power of $\log R$. This is achieved by considering a suitable amplitude-dependent wave envelope estimate, as was introduced in a recent paper of Guth and Maldague to demonstrate a small cap decoupling for the $(2+1)$ cone; we demonstrate that the version for $\mathbb{P}^1$ may be taken with a loss controlled by a power of $\log R$ as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00125 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Small cap decoupling for the parabola with logarithmic constant Johnsrude, Ben Classical Analysis and ODEs 42B10 We note that the subpolynomial factor for the $\ell^qL^p$ small cap decoupling constants for the truncated parabola $\mathbb{P}^1=\{(t,t^2):|t|\leq 1\}$ may be controlled by a suitable power of $\log R$. This is achieved by considering a suitable amplitude-dependent wave envelope estimate, as was introduced in a recent paper of Guth and Maldague to demonstrate a small cap decoupling for the $(2+1)$ cone; we demonstrate that the version for $\mathbb{P}^1$ may be taken with a loss controlled by a power of $\log R$ as well. |
| title | Small cap decoupling for the parabola with logarithmic constant |
| topic | Classical Analysis and ODEs 42B10 |
| url | https://arxiv.org/abs/2305.00125 |