On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality

Cordero-Erausquin, Dario ; Fradelizi, Matthieu  ; Langharst, Dylan 

Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e125

Résumé

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.

Détail

DOI : 10.1017/fms.2025.41

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