On a Santaló point for Nakamura-Tsuji's Laplace transform inequality
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912221152411648 |
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| author | Cordero-Erausquin, Dario Fradelizi, Matthieu Langharst, Dylan |
| author_facet | Cordero-Erausquin, Dario Fradelizi, Matthieu Langharst, Dylan |
| contents | Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santaló inequality in its functional form. Inspired by their method, based on the Fokker-Planck semi-group, we extend the inequality to non-even functions. We consider a well-chosen centering procedure by studying the infimum over translations in a double Laplace transform. This requires a new look on the existing methods and leads to several observations of independent interest on the geometry of the Laplace transform. Application to reverse hypercontractivity is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Santaló point for Nakamura-Tsuji's Laplace transform inequality Cordero-Erausquin, Dario Fradelizi, Matthieu Langharst, Dylan Functional Analysis Metric Geometry Primary: 52A40 and 44A10, Secondary: 35K05 and 52A21 Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santaló inequality in its functional form. Inspired by their method, based on the Fokker-Planck semi-group, we extend the inequality to non-even functions. We consider a well-chosen centering procedure by studying the infimum over translations in a double Laplace transform. This requires a new look on the existing methods and leads to several observations of independent interest on the geometry of the Laplace transform. Application to reverse hypercontractivity is also given. |
| title | On a Santaló point for Nakamura-Tsuji's Laplace transform inequality |
| topic | Functional Analysis Metric Geometry Primary: 52A40 and 44A10, Secondary: 35K05 and 52A21 |
| url | https://arxiv.org/abs/2409.05541 |