Remarks on the growth of Lp-norms of polynomials

  • S. G. Bobkov
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1745)

Abstract

We study the behaviour of constants in Khinchine-Kahane-type inequalities for polynomials in random vectors which have logarithmically concave distributions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A]
    Alesker S. (1999) Localization technique on the sphere and the Gromov-Milman theorem on the concentration phenomenon on uniformly convex sphere. Convex Geometric Analysis (Berkeley, CA, 1996), Math. Sci. Res. Inst. Publ., 34, Cambridge Univ. Press, CambridgeGoogle Scholar
  2. [B]
    Bobkov S.G. (1998) Isoperimetric and analytic inequalities for log-concave probability measures. Preprint. Ann. Probab., to appearGoogle Scholar
  3. [B-G]
    Bobkov S.G., Götze F. (1997) On moments of polynomials. Probab. Theory Appl. 42(3):518–520MathSciNetCrossRefMATHGoogle Scholar
  4. [Bor]
    Borell C. (1974) Convex measures on locally convex spaces. Ark. Math. 12:239–252MathSciNetCrossRefMATHGoogle Scholar
  5. [Bou]
    Bourgain, J. (1991) On the distribution of polynomials on high dimensional convex sets. Lecture Notes in Math. 1469:127–137MathSciNetCrossRefMATHGoogle Scholar
  6. [Gu]
    Guédon O. (1998) Kahane-Khinchine type inequalities for negative exponents. Preprint. Mathematika, to appearGoogle Scholar
  7. [G-M1]
    Gromov M., Milman V.D. (1983–84) Brunn theorem and a concentration of volume phenomena for symmetric convex bodies. GAFA Seminar Notes, Tel Aviv University, IsraelGoogle Scholar
  8. [G-M2]
    Gromov M., Milman V.D. (1987) Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces. Composition Math. 62:263–282MathSciNetMATHGoogle Scholar
  9. [K-L-S]
    Kannan R., Lovász L., Simonovits M. (1995) Isoperimetric problems for convex bodies and a localization lemma. Discrete and Comput. Geom. 13:541–559MathSciNetCrossRefMATHGoogle Scholar
  10. [L]
    Latala R. (1996) On the equivalence between geometric and arithmetic means for logconcave measures. Convex Geometric Analysis, Berkeley, CA, 123–127MATHGoogle Scholar
  11. [L-S]
    Lovász L., Simonovits M. (1993) Random walks in a convex body and an improved volume algorithm. Random Structures and Algorithms 4(3):359–412MathSciNetCrossRefMATHGoogle Scholar
  12. [M-S]
    Milman V.D., Schechtman G. (1986) Asymptotic theory of finite dimensional normed spaces. Lecture Notes in Math. 1200, Springer, BerlinMATHGoogle Scholar
  13. [P1]
    Prokhorov Yu.V. (1992) On polynomials in normally distributed random variables. Probab. Theory Appl. 37(4):692–694MathSciNetCrossRefMATHGoogle Scholar
  14. [P2]
    Prokhorov Yu.V. (1993) On polynomials in random variables that have the gamma distribution. Probab. Theory Appl. 38(1):198–202MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 2000

Authors and Affiliations

  • S. G. Bobkov
    • 1
  1. 1.Department of MathematicsSyktyvkar UniversitySyktyvkarRussia

Personalised recommendations