Introduces the L^p-Legendre transform and proves a functional L^p-Santaló inequality: after translation by the L^p-Santaló point, the L^p-Mahler integral of any convex function is bounded by that of the Gaussian |x|^2/2.
Ball, Logarithmically concave functions and sections of convex s ets in Rn, Studia Math
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$L^p$-Legendre Transforms and Mahler integrals: Asymptotics and the Fokker--Planck heat flow
Introduces the L^p-Legendre transform and proves a functional L^p-Santaló inequality: after translation by the L^p-Santaló point, the L^p-Mahler integral of any convex function is bounded by that of the Gaussian |x|^2/2.