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Some remarks on Urysohn's inequality and volume ratio of cotype 2-spaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1267)

Abstract

This note consists of two parts. In the first part, we give a new proof of Urysohn's inequality relating a volume ratio of a central symmetric convex body K and the euclidean ball to the integral average E K *. We use this inequality in the second part through entropy estimations to give a new and very simple proof of the result from [BM1] that the volume ratios of the cotype 2-spaces are uniformly bounded by a constant depending only on the cotype 2-constant of a space.

Keywords

  • Unit Ball
  • Convex Body
  • Isoperimetric Inequality
  • Euclidean Ball
  • Springer Lecture Note

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© 1987 Springer-Verlag

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Milman, V.D. (1987). Some remarks on Urysohn's inequality and volume ratio of cotype 2-spaces. In: Lindenstrauss, J., Milman, V.D. (eds) Geometrical Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078137

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  • DOI: https://doi.org/10.1007/BFb0078137

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18103-3

  • Online ISBN: 978-3-540-47771-6

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