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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.04500 |
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| _version_ | 1866916676067393536 |
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| author | Roysdon, Michael |
| author_facet | Roysdon, Michael |
| contents | Inspired by resolution of the Busemann-Petty problem (1956), we consider the following comparison problem for dual Radon transforms: Given a pair of continuous functions defined on the affine Grassmannian whose dual Radon transforms satisfy a pointwise inequality, can their $L^p$ norms be compared in a meaningful way? We characterize the solution to this problem for each $p\geq 1$, and as a consequence of our investigation, we prove reverse $L^p$-$L^q$-estimates for dual Radon transforms. In particular, we reverse an inequality of Solmon (1979). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Busemann-Petty Type Problem for Dual Radon Transforms Roysdon, Michael Functional Analysis Inspired by resolution of the Busemann-Petty problem (1956), we consider the following comparison problem for dual Radon transforms: Given a pair of continuous functions defined on the affine Grassmannian whose dual Radon transforms satisfy a pointwise inequality, can their $L^p$ norms be compared in a meaningful way? We characterize the solution to this problem for each $p\geq 1$, and as a consequence of our investigation, we prove reverse $L^p$-$L^q$-estimates for dual Radon transforms. In particular, we reverse an inequality of Solmon (1979). |
| title | A Busemann-Petty Type Problem for Dual Radon Transforms |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2504.04500 |