Volume formulas in Lp-spaces

Yehoram Gordon, Marius Junge

Research output: Contribution to journalArticlepeer-review


We extend classical volume formulas for ellipsoids and zonoids to p-sums of segments m 1/n 1/pn vol (∑ ⊕p[-xi, xi]) ∼cp n-1/p′ (∑ | det(xi)i∈I|p), i=1 card(I)=n where x1, . . . , xm are m vectors in ℝn, 1/p + 1/p′ = 1. According to the definition of Firey, the Minkowski p-sum of segments is given by m m m 1/p′ ∑ ⊕p[-xi, xi] = {∑ αixi| (∑ |αi|p) ≤ 1}. i=1 i=1 i=1

Original languageEnglish (US)
Pages (from-to)7-43
Number of pages37
Issue number1
StatePublished - 1997
Externally publishedYes


  • Banach spaces
  • Ideal norms
  • L spaces
  • Volume ratios

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Analysis
  • Mathematics(all)


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