An example related to the slicing inequality for general measures

Bo'az Klartag, Alexander Koldobsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For n∈N, let Sn be the smallest number S>0 satisfying the inequality ∫Kf≤S⋅|K|[Formula presented]⋅maxξ∈Sn−1⁡∫K∩ξf for all centrally-symmetric convex bodies K in Rn and all even, continuous probability densities f on K. Here |K| is the volume of K. It was proved in [16] that Sn≤2n, and in analogy with Bourgain's slicing problem, it was asked whether Sn is bounded from above by a universal constant. In this note we construct an example showing that Sn≥cn/log⁡log⁡n, where c>0 is an absolute constant. Additionally, for any 0<α<2 we describe a related example that satisfies the so-called ψα-condition.

Original languageEnglish
Pages (from-to)2089-2112
Number of pages24
JournalJournal of Functional Analysis
Issue number7
StatePublished - 1 Apr 2018


Dive into the research topics of 'An example related to the slicing inequality for general measures'. Together they form a unique fingerprint.

Cite this