Archive for Rational Mechanics and Analysis

, Volume 65, Issue 3, pp 275–288 | Cite as

Estimates of harmonic measure

  • Björn E. J. Dahlberg


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  1. 1.
    Agmon, S., A. Douglis & L. Nirenberg, “Estimates near the boundary of solutions of elliptic partial differential equations satisfying general boundary conditions”. Com. Pure Applied Math. 12, 623–727 (1959).Google Scholar
  2. 2.
    Carleson, L., “On the existence of boundary values of harmonic functions of several variables”. Ark. Mat. 4, 339–343 (1962).Google Scholar
  3. 3.
    Coifman, R. R. & C. Fefferman, “Weighted norm inequalities for maximal functions and singular integrals”. Studia Math., 51, 241–250 (1974).Google Scholar
  4. 4.
    Gehring, F. W., “The Lp-integrability of the partial derivatives of a quasiconformal mapping”. Acta Math. 130, 265–277 (1973).Google Scholar
  5. 5.
    Helms, L.L., “Introduction to potential theory”. New York: Wiley-Interscience 1969.Google Scholar
  6. 6.
    Hunt, R. & R.L. Wheeden, “On the boundary values of harmonic functions”. Trans. Amer. Math. Soc. 132, 307–322 (1968).Google Scholar
  7. 7.
    Hunt, R.A. & R.L. Wheeden, “Positive harmonic functions on Lipschitz domains”. Trans. Amer. Math. Soc. 147, 507–527 (1970).Google Scholar
  8. 8.
    Kemper, J.T., “A boundary Harnack principle for Lipschitz domains and the principle of positive singularities”. Comm. Pure Applied Math. 25, 247–255 (1972).Google Scholar
  9. 9.
    Naïm, L., Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel. Ann. Inst. Fourier (Grenoble), 7, 183–281 (1957).Google Scholar
  10. 10.
    Priwalow, I.I., “Randeigenschaften analytischer Funktionen”. Berlin: Deutscher Verlag der Wissenschaften 1956.Google Scholar
  11. 11.
    Saks, S., Theory of the integral. New York: Hafner Publishing Company 1937.Google Scholar
  12. 12.
    Stein, E.M., “Singular integrals and differentiability properties of functions”. New Jersey: Princeton University Press, Princeton 1970.Google Scholar
  13. 13.
    Warschawski, S.E. & G.E. Schober, “On conformal mapping of certain classes of Jordan domains”. Arch. Rational Mech. Anal. 22, 201–209 (1966).Google Scholar
  14. 14.
    Widman, K.-O., “Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic equations”. Math. Scand. 21, 17–37 (1967).Google Scholar
  15. 15.
    Ziemer, W.P., “Some remarks on harmonic measure in space”. Pac. J. Math. 55, 629–638 (1974).Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Björn E. J. Dahlberg
    • 1
  1. 1.Department of MathematicsUniversity of Göteborg, Göteborg Chalmers University of TechnologyFackSweden

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