Abstract
We prove that there exists an absolute constant C so that
for any p > 2, any \(n \in \mathbb{N},\) any convex body K that is the unit ball of an n-dimensional subspace of L p , and any measure μ with non-negative even continuous density in \(\mathbb{R}^{n}.\) Here ξ ⊥ is the central hyperplane perpendicular to a unit vector ξ ∈ S n−1, and | K | stands for volume.
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Acknowledgements
The first named author was partially supported by the US National Science Foundation, grant DMS-1265155.
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Koldobsky, A., Pajor, A. (2017). A Remark on Measures of Sections of \(\boldsymbol{L}_{p}\)-balls. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2169. Springer, Cham. https://doi.org/10.1007/978-3-319-45282-1_14
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DOI: https://doi.org/10.1007/978-3-319-45282-1_14
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