Local smoothing estimates for bilinear Fourier integral operators
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911491970564096 |
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| author | Cardona, Duván |
| author_facet | Cardona, Duván |
| contents | We formulate a local smoothing conjecture for bilinear Fourier integral operators in every dimension $d \ge 2,$ derived from the celebrated linear case due to Sogge, which we refer to as the \emph{bilinear smoothing conjecture}. We show that the linear local smoothing conjecture implies this bilinear version. As a consequence of our approach and due to the recent progress on the subject, we establish local smoothing estimates for Fourier integral operators in dimension $d=2,$ that is, on $\mathbb{R}^2_x \times \mathbb{R}_t$. Also, a partial progress is presented for the high-dimensional case $d\geq 3.$ In particular, our method allows us to deduce that the bilinear local smoothing conjecture holds for all odd dimensions $d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15667 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local smoothing estimates for bilinear Fourier integral operators Cardona, Duván Analysis of PDEs Functional Analysis We formulate a local smoothing conjecture for bilinear Fourier integral operators in every dimension $d \ge 2,$ derived from the celebrated linear case due to Sogge, which we refer to as the \emph{bilinear smoothing conjecture}. We show that the linear local smoothing conjecture implies this bilinear version. As a consequence of our approach and due to the recent progress on the subject, we establish local smoothing estimates for Fourier integral operators in dimension $d=2,$ that is, on $\mathbb{R}^2_x \times \mathbb{R}_t$. Also, a partial progress is presented for the high-dimensional case $d\geq 3.$ In particular, our method allows us to deduce that the bilinear local smoothing conjecture holds for all odd dimensions $d$. |
| title | Local smoothing estimates for bilinear Fourier integral operators |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2601.15667 |