Mathematische Annalen

, Volume 219, Issue 3, pp 233–260 | Cite as

Optimal Lipschitz andLp regularity for the equation\(\bar \partial u = f\) on strongly pseudo-convex domains

  • Steven G. Krantz
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fefferman, Ch.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Inventiones Math.26, 1–65 (1974)Google Scholar
  2. 2.
    Folland, G., Kohn, J. J.: The Nuumann problem for the Cauchy-Riemann complex. Princeton: Princeton University Press 1972Google Scholar
  3. 3.
    Folland, G., Stein, E. M.: Estimates for the ∂b complex and analysis on the Heisenberg group. Comm. Pure and Applied Math. (to appear)Google Scholar
  4. 4.
    Grauert, H., Lieb, I.: Das Ramirezsche Integral und die Gleichung\(\bar \partial u = \alpha \) im Bereich der beschränkten Formen. Rice Univ. Studies56, 29–50 (1970)Google Scholar
  5. 5.
    Henkin, G. M.: Integral representations of functions holomorphic in strictly pseudo-convex domains and some applications. Mat. Sb.78 (120), 611–632 (1969); Math. U.S.S.R. Sb.7, 597–616 (1969)Google Scholar
  6. 6.
    Henkin, G. M.: Integral representations of functions holomorphic in strictly pseudo-convex domains and applications to the ∂ problem. Mat. Sb.82, (124), 300–308 (1970); Math. U.S.S.R. Sb.11, 273–281 (1970)Google Scholar
  7. 7.
    Henkin, G. M., Romanov, A. V.: Exact Hölder estimates of solutions of the\(\bar \partial \) equation. Izvestija Akad. SSSR, Ser. Mat.35, 1171–1183 (1971); Math. USSR Sb.5, 1180–1192 (1971)Google Scholar
  8. 8.
    Hörmander, L.: An introduction to complex analysis in several variables. Princeton: Van Nostrand 1966Google Scholar
  9. 9.
    Kerzman, N.: Hölder andL p estimates for solutions of\(\bar \partial u = f\) on strongly pseudo-convex domains. Comm. Pure Appl. Math24, 301–379 (1971)Google Scholar
  10. 10.
    Koppelman, W.: The Cauchy integral for functions of several complex variables. Bull. Amer. Math. Soc.73, 373–377 (1967)Google Scholar
  11. 11.
    Krantz, S.: Optimal Lipschitz andL p estimates on strongly pseudo-convex domains. Princeton University Ph. D. Thesis 1974Google Scholar
  12. 12.
    Lieb, I.: Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudo convexen Gebieten: Beschränkte Lösungen. Math. Annalen190, 6–44 (1970)Google Scholar
  13. 13.
    Lieb, I.: Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudo convexen Gebieten: Stetige Randwerte. Math. Annalen199, 241–256 (1972)Google Scholar
  14. 14.
    Siu, Y. T.: The\(\bar \partial \) problem with uniform bounds on derivatives. Math. Annalen207, 163–176 (1974)Google Scholar
  15. 15.
    Stein, E. M.: Lectures on singular integrals and pseudodifferential operators. Princeton University Press (to appear)Google Scholar
  16. 16.
    Stein, E. M.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press 1970Google Scholar
  17. 17.
    Stein, E. M.: Singular integrals and estimates for the Cauchy-Riemann equations. Bull. Amer. Math. Soc.79, 440–445 (1973)Google Scholar
  18. 18.
    Zygmund, A.: Trigometric series, second ed. Cambridge: Cambridge University Press 1968Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Steven G. Krantz
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

Personalised recommendations