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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Partially supported by Spanish grants MTM2016-77710-P, DGA E26 17R and IUMA.
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Alonso-Gutiérrez, D., Bernués, J. The square negative correlation property on \(\ell_p^n\)- balls. Isr. J. Math. 230, 895–917 (2019). https://doi.org/10.1007/s11856-019-1840-3
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DOI: https://doi.org/10.1007/s11856-019-1840-3