Orthogonal projection, dual Furstenberg problem, and discretized sum-product
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916511665356800 |
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| author | Li, Longhui Liu, Bochen |
| author_facet | Li, Longhui Liu, Bochen |
| contents | In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via $L^p$ estimates of orthogonal projections. Examples are also discussed. Moreover, compared with general sets, we find that special structure like Cartesian product has better $L^p$-behavior. This leads to improvement on some discretized sum-product estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal projection, dual Furstenberg problem, and discretized sum-product Li, Longhui Liu, Bochen Classical Analysis and ODEs In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via $L^p$ estimates of orthogonal projections. Examples are also discussed. Moreover, compared with general sets, we find that special structure like Cartesian product has better $L^p$-behavior. This leads to improvement on some discretized sum-product estimates. |
| title | Orthogonal projection, dual Furstenberg problem, and discretized sum-product |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.15784 |