Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A.P. Calderón, "Cauchy integrals on Lipschitz curves and related topics," Proc. Nat. Acad. Sci. U.S.A. 74(1977), 1324–1327.
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.
G. David, "Opérateurs integraux singuliers sur certaines courbes du plan complexe." Ann. Scient. Ec. Norm. Sup. 17(1984), 157–189.
_____, "Une minoration de la norme de l’operateur de Cauchy sur les graphes lipschitziens," to appear T.A.M.S.
G. David and J.L. Journé, “A boundedness criterion for general Calderón-Zygmund operators," Ann. Math. 120(1984), 371–397.
G. David, J.L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para acrétives et interpolation," Revista Matemática Iberoamericana 4(1985), 1–56.
W. Feller, An Introduction to probability theory and its applications, Vol. 1, John Wiley and Sons, Inc., 1968.
J. Garnett, "Positive length but zero analytic capacity," P.A.M.S. 24(1970), 696–699.
_____, Bounded analytic functions, Academic Press, 1981.
D. Jerison and C. Kenig, "Hardy spaces, A∞, and singular integrals on chord-arc domains," Math. Scand. 50(1982), 221–247.
P.W. Jones and S. Semmes, "An elementary proof of the boundedness of Cauchy integrals on Lipschitz curves," preprint.
C. Kenig, "Weighted Hp spaces on Lipschitz domains," Amer. J. Math. 102(1980), 129–163.
A. Uchiyama, "A constructive proof of the Fefferman-Stein decomposition of BMO(Rn)," Acta Math. 148(1982), 215–241.
M. Weiss, "The law of the iterated logarithm for lacunary trigonometric series, T.A.M.S. 91(1959), 444–469.
M. Zinsmeister, "Domaines reguliers du plan," Ann. Inst. Fourier, Grenoble, 35(1985), 49–55.
N.G. Makarov, "On the distortion of boundary sets under conformal mappings," Proc. London Math. Soc. 51(1985), 369–384.
P. Mattila, "Smooth maps, null sets for integral geometric measure and analytic capacity," Ann. Math. 123(1986), 303–309.
T. Murai, A real variable method for the Cauchy transform and applications to analytic capacity, to appear in Springer Lecture Notes series.
F. Przytyeki, M. Urbanski, A. Zdunik, Harmonic, Hausdorff, and Gibbs measures on repellers for holomorphic maps, preprint 1986.
R. Salem and A. Zygmund, "La loi du logarithme iteré pour les séries trigonometriques lacunaires," Bull. Sci. Math. 74(1950), 209–224.
E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, 1970.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Jones, P.W. (1989). Square functions, Cauchy integrals, analytic capacity, and harmonic measure. In: García-Cuerva, J. (eds) Harmonic Analysis and Partial Differential Equations. Lecture Notes in Mathematics, vol 1384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086793
Download citation
DOI: https://doi.org/10.1007/BFb0086793
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51460-2
Online ISBN: 978-3-540-48134-8
eBook Packages: Springer Book Archive