On trilinear singular Brascamp-Lieb integrals
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913569471201280 |
|---|---|
| author | Becker, Lars Durcik, Polona Lin, Fred Yu-Hsiang |
| author_facet | Becker, Lars Durcik, Polona Lin, Fred Yu-Hsiang |
| contents | We classify all trilinear singular Brascamp-Lieb forms, completing the classification in the two dimensional case by Demeter and Thiele in arXiv:0803.1268. We use known results in the representation theory of finite dimensional algebras, namely the classification of indecomposable representations of the four subspace quiver. Our classification lays out a roadmap for achieving bounds for all degenerate higher dimensional bilinear Hilbert transforms. As another step towards this goal, we prove new bounds for a particular class of forms that arises as a natural next candidate from our classification. We further prove conditional bounds for forms associated with mutually related representations. For this purpose we develop a method of rotations that allows us to decompose any homogeneous $d$-dimensional singular integral kernel into $(d-1)$-dimensional kernels on hyperplanes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00141 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On trilinear singular Brascamp-Lieb integrals Becker, Lars Durcik, Polona Lin, Fred Yu-Hsiang Classical Analysis and ODEs 42B20, 42B15 We classify all trilinear singular Brascamp-Lieb forms, completing the classification in the two dimensional case by Demeter and Thiele in arXiv:0803.1268. We use known results in the representation theory of finite dimensional algebras, namely the classification of indecomposable representations of the four subspace quiver. Our classification lays out a roadmap for achieving bounds for all degenerate higher dimensional bilinear Hilbert transforms. As another step towards this goal, we prove new bounds for a particular class of forms that arises as a natural next candidate from our classification. We further prove conditional bounds for forms associated with mutually related representations. For this purpose we develop a method of rotations that allows us to decompose any homogeneous $d$-dimensional singular integral kernel into $(d-1)$-dimensional kernels on hyperplanes. |
| title | On trilinear singular Brascamp-Lieb integrals |
| topic | Classical Analysis and ODEs 42B20, 42B15 |
| url | https://arxiv.org/abs/2411.00141 |