Skip to main content
SpringerLink
Log in
Book cover

Geometric Aspects of Functional Analysis pp 27–35Cite as

Remarks on the growth of L p-norms of polynomials

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((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.

The work was partially supported by a grant of the Russian Foundation for Fundamental Research.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   52.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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, Cambridge

    Google Scholar 

  2. Bobkov S.G. (1998) Isoperimetric and analytic inequalities for log-concave probability measures. Preprint. Ann. Probab., to appear

    Google Scholar 

  3. Bobkov S.G., Götze F. (1997) On moments of polynomials. Probab. Theory Appl. 42(3):518–520

    Article  MathSciNet  MATH  Google Scholar 

  4. Borell C. (1974) Convex measures on locally convex spaces. Ark. Math. 12:239–252

    Article  MathSciNet  MATH  Google Scholar 

  5. Bourgain, J. (1991) On the distribution of polynomials on high dimensional convex sets. Lecture Notes in Math. 1469:127–137

    Article  MathSciNet  MATH  Google Scholar 

  6. Guédon O. (1998) Kahane-Khinchine type inequalities for negative exponents. Preprint. Mathematika, to appear

    Google Scholar 

  7. 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, Israel

    Google Scholar 

  8. Gromov M., Milman V.D. (1987) Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces. Composition Math. 62:263–282

    MathSciNet  MATH  Google Scholar 

  9. Kannan R., Lovász L., Simonovits M. (1995) Isoperimetric problems for convex bodies and a localization lemma. Discrete and Comput. Geom. 13:541–559

    Article  MathSciNet  MATH  Google Scholar 

  10. Latala R. (1996) On the equivalence between geometric and arithmetic means for logconcave measures. Convex Geometric Analysis, Berkeley, CA, 123–127

    MATH  Google Scholar 

  11. Lovász L., Simonovits M. (1993) Random walks in a convex body and an improved volume algorithm. Random Structures and Algorithms 4(3):359–412

    Article  MathSciNet  MATH  Google Scholar 

  12. Milman V.D., Schechtman G. (1986) Asymptotic theory of finite dimensional normed spaces. Lecture Notes in Math. 1200, Springer, Berlin

    MATH  Google Scholar 

  13. Prokhorov Yu.V. (1992) On polynomials in normally distributed random variables. Probab. Theory Appl. 37(4):692–694

    Article  MathSciNet  MATH  Google Scholar 

  14. Prokhorov Yu.V. (1993) On polynomials in random variables that have the gamma distribution. Probab. Theory Appl. 38(1):198–202

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Syktyvkar University, 167001, Syktyvkar, Russia

    S. G. Bobkov

Authors
  1. S. G. Bobkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Vitali D. Milman Gideon Schechtman

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag

About this chapter

Cite this chapter

Bobkov, S.G. (2000). Remarks on the growth of L p-norms of polynomials. In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107206

Download citation

  • DOI: https://doi.org/10.1007/BFb0107206

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41070-6

  • Online ISBN: 978-3-540-45392-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation