Grünbaum‐type inequality for log‐concave functions. Issue 4 (17th July 2018)

• Record Type: Journal Article
• Authors: Meyer, Mathieu; Nazarov, Fedor; Ryabogin, Dmitry; Yaskin, Vladyslav
• Is Part Of: Bulletin of the London Mathematical Society. Volume 50:Issue 4(2018)
• Page Start: 745
• Page End: 752
• Publication Date: 2018-07-17
• Subjects: 26B25 -- 26B15 -- 26D15 -- 52A20 (primary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12175
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: Let f be an integrable log‐concave function on R n with the center of mass at the origin. We show that ∫ 0 ∞ f ( s θ ) d s ⩾ e − n ∫ − ∞ ∞ f ( s θ ) d s for every θ ∈ S n − 1, and the constant e − n is the best possible.