Advertisement

Square functions, Cauchy integrals, analytic capacity, and harmonic measure

  • Peter W. Jones
Main Lectures
Part of the Lecture Notes in Mathematics book series (LNM, volume 1384)

Keywords

Lipschitz Domain Harmonic Measure Iterate Logarithm Carleson Measure Analytic Capacity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [C]
    A.P. Calderón, "Cauchy integrals on Lipschitz curves and related topics," Proc. Nat. Acad. Sci. U.S.A. 74(1977), 1324–1327.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [Co,Mc,Me]
    R. Coifman, A. McIntosh, and Y. Meyer, "L, intégrale de Cauchy définit un opéateur borné sur L2 pour les courbes lipschitziennes," Ann. Math. 116(1982), 361–387.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [D1]
    G. David, "Opérateurs integraux singuliers sur certaines courbes du plan complexe." Ann. Scient. Ec. Norm. Sup. 17(1984), 157–189.zbMATHGoogle Scholar
  4. [D2]
    _____, "Une minoration de la norme de l’operateur de Cauchy sur les graphes lipschitziens," to appear T.A.M.S.Google Scholar
  5. [D,J]
    G. David and J.L. Journé, “A boundedness criterion for general Calderón-Zygmund operators," Ann. Math. 120(1984), 371–397.CrossRefzbMATHGoogle Scholar
  6. [D,J.Se]
    G. David, J.L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para acrétives et interpolation," Revista Matemática Iberoamericana 4(1985), 1–56.CrossRefzbMATHGoogle Scholar
  7. [F]
    W. Feller, An Introduction to probability theory and its applications, Vol. 1, John Wiley and Sons, Inc., 1968.Google Scholar
  8. [G1]
    J. Garnett, "Positive length but zero analytic capacity," P.A.M.S. 24(1970), 696–699.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [G2]
    _____, Bounded analytic functions, Academic Press, 1981.Google Scholar
  10. [Je,K]
    D. Jerison and C. Kenig, "Hardy spaces, A, and singular integrals on chord-arc domains," Math. Scand. 50(1982), 221–247.MathSciNetzbMATHGoogle Scholar
  11. [Jo,Se]
    P.W. Jones and S. Semmes, "An elementary proof of the boundedness of Cauchy integrals on Lipschitz curves," preprint.Google Scholar
  12. [K]
    C. Kenig, "Weighted Hp spaces on Lipschitz domains," Amer. J. Math. 102(1980), 129–163.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [U]
    A. Uchiyama, "A constructive proof of the Fefferman-Stein decomposition of BMO(Rn)," Acta Math. 148(1982), 215–241.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [W]
    M. Weiss, "The law of the iterated logarithm for lacunary trigonometric series, T.A.M.S. 91(1959), 444–469.MathSciNetzbMATHGoogle Scholar
  15. [Z]
    M. Zinsmeister, "Domaines reguliers du plan," Ann. Inst. Fourier, Grenoble, 35(1985), 49–55.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [Mak]
    N.G. Makarov, "On the distortion of boundary sets under conformal mappings," Proc. London Math. Soc. 51(1985), 369–384.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [Mat]
    P. Mattila, "Smooth maps, null sets for integral geometric measure and analytic capacity," Ann. Math. 123(1986), 303–309.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [Mu]
    T. Murai, A real variable method for the Cauchy transform and applications to analytic capacity, to appear in Springer Lecture Notes series.Google Scholar
  19. [P,Ur,Zd]
    F. Przytyeki, M. Urbanski, A. Zdunik, Harmonic, Hausdorff, and Gibbs measures on repellers for holomorphic maps, preprint 1986.Google Scholar
  20. [Sa,Zy]
    R. Salem and A. Zygmund, "La loi du logarithme iteré pour les séries trigonometriques lacunaires," Bull. Sci. Math. 74(1950), 209–224.MathSciNetzbMATHGoogle Scholar
  21. [St]
    E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, 1970.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Peter W. Jones
    • 1
  1. 1.Yale UniversityNew Haven

Personalised recommendations