The John inclusion for log-concave functions
Abstract
John's inclusion states that a convex body in R d can be covered by the d -dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-concave functions. As a byproduct of our approach, we establish the following asymptotically tight inequality: For any log-concave function f with finite, positive integral, there exist a positive definite matrix A , a point a ∈ R d , and a positive constant α such that χ B d ( x ) ≤ α f ( A ( x − a ) ) ≤ d + 1 ⋅ e − | x | d + 2 + ( d + 1 ) , where χ B d is the indicator function of the unit ball B d .
Fields of Study & Subjects
Point processes and geometric inequalities
Mathematical Inequalities and Applications
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 559
- Issue
- 1
- Pages
- 130441–130441
- Publication date
- 15 January 2026
- Language
- EN