Multiple convolutions and multilinear fractal Fourier extension estimates
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_ | 1866908824838864896 |
|---|---|
| author | Oliveira, Itamar de Orellana, Ana E. |
| author_facet | Oliveira, Itamar de Orellana, Ana E. |
| contents | The classical Stein--Tomas theorem extends the theory of linear Fourier restriction estimates from smooth manifolds to fractal measures exhibiting Fourier decay. In the multilinear setting, transversality allows for Fourier extension estimates that go beyond those implied by the linear theory to hold. We establish a multilinear Fourier extension estimate for measures whose convolution belongs to an $L^p$ space, applicable to known results by Shmerkin and Solomyak that exploit `transversality' between self-similar measures. Moreover, we generalise work by Hambrook--Łaba and Chen from the linear setting to obtain Knapp-type examples for multilinear estimates; we obtain two necessary conditions: one in terms of the upper box dimension of the measures' supports, and another one in terms of their Fourier decay and a ball condition. In particular, these conditions give a more restrictive range compared with previously known results whenever the convolution of the measures at play is singular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08568 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiple convolutions and multilinear fractal Fourier extension estimates Oliveira, Itamar de Orellana, Ana E. Classical Analysis and ODEs Functional Analysis Metric Geometry primary: 28A80, 42B10, secondary: 28A75, 28A78 The classical Stein--Tomas theorem extends the theory of linear Fourier restriction estimates from smooth manifolds to fractal measures exhibiting Fourier decay. In the multilinear setting, transversality allows for Fourier extension estimates that go beyond those implied by the linear theory to hold. We establish a multilinear Fourier extension estimate for measures whose convolution belongs to an $L^p$ space, applicable to known results by Shmerkin and Solomyak that exploit `transversality' between self-similar measures. Moreover, we generalise work by Hambrook--Łaba and Chen from the linear setting to obtain Knapp-type examples for multilinear estimates; we obtain two necessary conditions: one in terms of the upper box dimension of the measures' supports, and another one in terms of their Fourier decay and a ball condition. In particular, these conditions give a more restrictive range compared with previously known results whenever the convolution of the measures at play is singular. |
| title | Multiple convolutions and multilinear fractal Fourier extension estimates |
| topic | Classical Analysis and ODEs Functional Analysis Metric Geometry primary: 28A80, 42B10, secondary: 28A75, 28A78 |
| url | https://arxiv.org/abs/2602.08568 |