Mathematische Zeitschrift

, Volume 246, Issue 4, pp 655–666 | Cite as

Littlewood-Paley functions associated to second order elliptic operators

Article

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 ℝ n .

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References

  1. 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)MATHGoogle Scholar
  2. 2.
    Auscher, P., Tchamitchian, P.: Square root problem for divergence operators and related topics. Astérisque 249, (1998)Google Scholar
  3. 3.
    Blunck S., Kunstmann, P.C.: Calderón-Zygmund theory for non-integral operators and H functional calculus. To appear in Rev. Mat. IberoamGoogle Scholar
  4. 4.
    Coulhn, T., Duong, X.T.: Littlewood-Paley-Stein functions on complete Riemannian manifolds. Studia Math. 154, 37–57 (2003)Google Scholar
  5. 5.
    Duong, X.T., McIntosh, A.: Singular integral operators with non-smooth kernels on irregular domains. Rev. Mat. Iberoamericana 15, 233–265 (1999)MathSciNetMATHGoogle Scholar
  6. 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. 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. 210–231Google Scholar
  8. 8.
    Stein, E.M.: Singular integral and differentiability properties of functions. Princeton U.P. 30, (1970)Google Scholar
  9. 9.
    Yan, L.X.: A remark on Littlewood-Paley g-function. Bull. Austral. Math. Soc. 66, 33–41 (2002)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsZhongshan UniversityGuangzhouP.R. China

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