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arXiv · 2409.05541

On a Santal\'o point for Nakamura-Tsuji's Laplace transform inequality

Dario Cordero-Erausquin·Matthieu Fradelizi·Dylan Langharst
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Abstract

Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santal\'o 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.

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Dario Cordero-Erausquin, Matthieu Fradelizi, Dylan Langharst. 2024-09-09. On a Santal\'o point for Nakamura-Tsuji's Laplace transform inequality. https://arxiv.org/abs/2409.05541

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