An example related to the slicing inequality for general measures

Bo'az Klartag, Alexander Koldobsky

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Pages (from-to)2089-2112
Number of pages24
JournalJournal of Functional Analysis
Issue number7
Early online date6 Sep 2017
StatePublished - 1 Apr 2018

All Science Journal Classification (ASJC) codes

  • Analysis


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