Skip to main content
SpringerLink
Log in

Nash inequalities for general symmetric forms

  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincaré and the logarithmic Sobolev inequalities in the present context.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J Nash. Continuity of solutions of parabolic and elliptic equations. Amer J Math, 1958, 80: 931–954

    Article  MATH  Google Scholar 

  2. E A Carlen, S Kusuoka, D W Stroock. Upper bounds for symmetric Markov transition functions. Ann Inst Henri Poincaré, 1987, (2): 245–287

  3. M F Chen. From Markov Chains to Non-Equilibrium Particle Systems. World Scientific, 1992

  4. D Bakry. L’hypercontractivité et son utilisation en théorie des semigroupes. LNM, Springer, 1992, 1581

    Google Scholar 

  5. N Th Varopoulos. Isoperimetric inequalities and Markov chains. J Funct Anal, 1985, 63: 215–239

    Article  MATH  Google Scholar 

  6. L Saloff-Coste. Lectures on finite Markov chains. LNM Springer-Verlag, 1997, 1665: 301–413

    Google Scholar 

  7. M F Chen, F Y Wang. Cheeger’s inequalities for general symmetric forms and existence criteria for spectral gap. Preprint Abstract: Chin Sci Bulletin, 1998, 43(14): 1475–1477 (Chinese Edition); 1998, 43(18): 1516–1519 (English Edition)

    Google Scholar 

  8. F Y Wang. Sobolev type inequalities for general symmetric forms. to appear in Proc Amer Math Soc, 1999

  9. M F Chen. Estimation of spectral gap for Markov chains. Acta Math Sin New Ser, 1996, 12(4): 337–360

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, 100875, Beijing, P. R. China

    Mufa Chen

Authors
  1. Mufa Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by NSFC (No. 19631060), Math. Tian Yuan Found., Qiu Shi Sci. & Tech. Found., RFDP and MCME

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, M. Nash inequalities for general symmetric forms. Acta Mathematica Sinica 15, 353–370 (1999). https://doi.org/10.1007/BF02650730

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02650730

Keywords

1991MR Subject Classification

Search

Navigation