On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality
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 functi...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000416/type/journal_article |
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| author | Dario Cordero-Erausquin Matthieu Fradelizi Dylan Langharst |
| author_facet | Dario Cordero-Erausquin Matthieu Fradelizi Dylan Langharst |
| author_sort | Dario Cordero-Erausquin |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-d7f9e9e2fb9545648d216d843d94b0df |
| institution | DOAJ |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-d7f9e9e2fb9545648d216d843d94b0df2025-08-20T02:46:44ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.41On a Santaló point for Nakamura-Tsuji’s Laplace transform inequalityDario Cordero-Erausquin0Matthieu Fradelizi1https://orcid.org/0000-0001-9362-6819Dylan Langharst2https://orcid.org/0000-0002-4767-3371Institut de Mathématiques de Jussieu (IMJ-PRG), Sorbonne Université, CNRS, 4 Place Jussieu, Paris, 75252, France; URL: https://webusers.imj-prg.fr/~dario.cordero/LAMA, Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, Marne-la-Vallée, F-77447, France; E-mail:Institut de Mathématiques de Jussieu (IMJ-PRG), Sorbonne Université, CNRS, 4 Place Jussieu, Paris, 75252, France; E-mail: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.https://www.cambridge.org/core/product/identifier/S2050509425000416/type/journal_article52A4044A1035K0552A21 |
| spellingShingle | Dario Cordero-Erausquin Matthieu Fradelizi Dylan Langharst On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality Forum of Mathematics, Sigma 52A40 44A10 35K05 52A21 |
| title | On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality |
| title_full | On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality |
| title_fullStr | On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality |
| title_full_unstemmed | On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality |
| title_short | On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality |
| title_sort | on a santalo point for nakamura tsuji s laplace transform inequality |
| topic | 52A40 44A10 35K05 52A21 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425000416/type/journal_article |
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