Brascamp--Lieb inequalities for fractal dimensions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914581448753152 |
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| author | Fraser, Jonathan M. |
| author_facet | Fraser, Jonathan M. |
| contents | We use the Brascamp--Lieb inequality from functional analysis to prove novel inequalities for the upper box, packing, and Assouad dimensions of fractal sets in terms of the dimensions of certain projections. Analogous inequalities do not hold for Hausdorff or lower box dimensions. We apply these fractal Brascamp--Lieb inequalities to establish new exceptional set estimates for orthogonal projections and to provide sharp dimension estimates for certain constrained sumsets. We also establish analogous nonlinear inequalities via the nonlinear Brascamp--Lieb inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20412 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brascamp--Lieb inequalities for fractal dimensions Fraser, Jonathan M. Functional Analysis Classical Analysis and ODEs Metric Geometry 28A80, 28A78, 26D20, 11B30 We use the Brascamp--Lieb inequality from functional analysis to prove novel inequalities for the upper box, packing, and Assouad dimensions of fractal sets in terms of the dimensions of certain projections. Analogous inequalities do not hold for Hausdorff or lower box dimensions. We apply these fractal Brascamp--Lieb inequalities to establish new exceptional set estimates for orthogonal projections and to provide sharp dimension estimates for certain constrained sumsets. We also establish analogous nonlinear inequalities via the nonlinear Brascamp--Lieb inequality. |
| title | Brascamp--Lieb inequalities for fractal dimensions |
| topic | Functional Analysis Classical Analysis and ODEs Metric Geometry 28A80, 28A78, 26D20, 11B30 |
| url | https://arxiv.org/abs/2605.20412 |