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Israel Journal of Mathematics

, Volume 230, Issue 2, pp 895–917 | Cite as

The square negative correlation property on \(\ell_p^n\)- balls

  • David Alonso-Gutiérrez
  • Julio BernuésEmail author
Article
  • 8 Downloads

Abstract

In this paper we prove that for any p ∈ [2,∞) the \(\ell_p^n\) unit ball, \(B_p^n\), satisfies the square negative correlation property with respect to every orthonormal basis, while we show it is not always the case for 1 ≤ p ≤ 2. In order to do that we regard \(B_p^n\) as the orthogonal projection of \(B_p^{n+1}\) onto the hyperplane \(e_{n+1}^\perp\). We will also study the orthogonal projection of \(B_p^n\) onto the hyperplane orthogonal to the diagonal vector (1, …, 1). In this case, the property holds for all p ≥ 1 and n large enough.

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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Área de análisis matemático, Departamento de matemáticas, IUMA Facultad de CienciasUniversidad de ZaragozaZaragozaSpain

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