Skip to main content
SpringerLink
Log in

Littlewood-Paley functions associated to second order elliptic operators

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

Abstract.

We prove L p-estimates for the Littlewood-Paley function associated with a second order divergence form operator L=−div A∇ with bounded measurable complex coefficients in ℝn.

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. Auscher, P., Hofmann, S., Lacey, M., McIntosh, A., Tchamitchian, P.: The solution of the Kato’s square root problem for second elliptic operators on ℝn. Ann. Math. 156, 633–654 (2002)

    MATH  Google Scholar 

  2. Auscher, P., Tchamitchian, P.: Square root problem for divergence operators and related topics. Astérisque 249, (1998)

  3. Blunck S., Kunstmann, P.C.: Calderón-Zygmund theory for non-integral operators and H ∞ functional calculus. To appear in Rev. Mat. Iberoam

  4. Coulhn, T., Duong, X.T.: Littlewood-Paley-Stein functions on complete Riemannian manifolds. Studia Math. 154, 37–57 (2003)

    Google Scholar 

  5. Duong, X.T., McIntosh, A.: Singular integral operators with non-smooth kernels on irregular domains. Rev. Mat. Iberoamericana 15, 233–265 (1999)

    MathSciNet  MATH  Google Scholar 

  6. Hofmann, S., Martell, J.M.: L p bounds for Riesz transforms and square roots associated to second order elliptic operators. Pub. Mat. 47, 497–515 (2003)

    Google Scholar 

  7. McIntosh, A.: Operators which have an H ∞-calculus. Miniconference on Operator Theory and Partial Differential Equations, 1986, Proceedings of the Centre for Mathematical Analysis, ANU, Canberra, 1986, pp. 210–231

  8. Stein, E.M.: Singular integral and differentiability properties of functions. Princeton U.P. 30, (1970)

  9. Yan, L.X.: A remark on Littlewood-Paley g-function. Bull. Austral. Math. Soc. 66, 33–41 (2002)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, Guangzhou, 510275, P.R. China

    Lixin Yan

Authors
  1. Lixin Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lixin Yan.

Additional information

Mathematics Subject Classification (2000):42B20, 35J15

The author is partially supported by NSF of China (Grant No. 10371134) and SRF for ROCS, SEM.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yan, L. Littlewood-Paley functions associated to second order elliptic operators. Math. Z. 246, 655–666 (2004). https://doi.org/10.1007/s00209-003-0606-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-003-0606-z

Keywords

Search

Navigation