Abstract
We establish new functional versions of the Blaschke–Santaló inequality on the volume product of a convex body which generalize to the non-symmetric setting an inequality of Ball [Isometric problems in ℓ p and sections of convex sets. PhD Dissertation, Cambridge, 1986] and we give a simple proof of the case of equality. As a corollary, we get some inequalities for log-concave functions and Legendre transforms which extend the recent result of Artstein et al. [Mathematika 51:33–48, 2004], with its equality case.
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Fradelizi, M., Meyer, M. Some functional forms of Blaschke–Santaló inequality. Math. Z. 256, 379–395 (2007). https://doi.org/10.1007/s00209-006-0078-z
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DOI: https://doi.org/10.1007/s00209-006-0078-z