Sparse Bounds for Rough Fourier Integral Operators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912970949263360 |
|---|---|
| author | Banzi, Wellars Minani, Froduald Mukeshimana, Solange Rule, David |
| author_facet | Banzi, Wellars Minani, Froduald Mukeshimana, Solange Rule, David |
| contents | We proof pointwise bounds for rough Fourier integral operators by the $L^p$ Hardy-Littlewood maximal function. We assume the Fourier integral operators have amplitudes in $L^\infty S^m_ρ$ and phases $φ$ such that $φ(x,ξ) - x\cdotξ\in L^\infty Φ^1$, and assume a non-degeneracy condition on the matrix $\partial^2_ξφ(x,ξ)$. The pointwise bound holds when \begin{equation*}
m < -\fracρ{2}(n-1) - \fracρ{p} - \frac{n}{p}(1-ρ), \end{equation*} which is known to a be sharp condition on $m$ when $ρ=1$, modulo the end-point. Making use of this pointwise bound and known $L^p$ boundedness results when the phase satisfies an additional non-degeneracy condition, we go on to prove sparse form bounds for these operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16460 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sparse Bounds for Rough Fourier Integral Operators Banzi, Wellars Minani, Froduald Mukeshimana, Solange Rule, David Classical Analysis and ODEs Analysis of PDEs 35S30, 42B20, 45P05, 42B37 We proof pointwise bounds for rough Fourier integral operators by the $L^p$ Hardy-Littlewood maximal function. We assume the Fourier integral operators have amplitudes in $L^\infty S^m_ρ$ and phases $φ$ such that $φ(x,ξ) - x\cdotξ\in L^\infty Φ^1$, and assume a non-degeneracy condition on the matrix $\partial^2_ξφ(x,ξ)$. The pointwise bound holds when \begin{equation*} m < -\fracρ{2}(n-1) - \fracρ{p} - \frac{n}{p}(1-ρ), \end{equation*} which is known to a be sharp condition on $m$ when $ρ=1$, modulo the end-point. Making use of this pointwise bound and known $L^p$ boundedness results when the phase satisfies an additional non-degeneracy condition, we go on to prove sparse form bounds for these operators. |
| title | Sparse Bounds for Rough Fourier Integral Operators |
| topic | Classical Analysis and ODEs Analysis of PDEs 35S30, 42B20, 45P05, 42B37 |
| url | https://arxiv.org/abs/2603.16460 |