Skip to main content
Log in

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

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Fefferman, Ch.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Inventiones Math.26, 1–65 (1974)

    Google Scholar 

  2. Folland, G., Kohn, J. J.: The Nuumann problem for the Cauchy-Riemann complex. Princeton: Princeton University Press 1972

    Google Scholar 

  3. Folland, G., Stein, E. M.: Estimates for the ∂ b complex and analysis on the Heisenberg group. Comm. Pure and Applied Math. (to appear)

  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. 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. 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. 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. Hörmander, L.: An introduction to complex analysis in several variables. Princeton: Van Nostrand 1966

    Google Scholar 

  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. Koppelman, W.: The Cauchy integral for functions of several complex variables. Bull. Amer. Math. Soc.73, 373–377 (1967)

    Google Scholar 

  11. Krantz, S.: Optimal Lipschitz andL p estimates on strongly pseudo-convex domains. Princeton University Ph. D. Thesis 1974

  12. Lieb, I.: Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudo convexen Gebieten: Beschränkte Lösungen. Math. Annalen190, 6–44 (1970)

    Google Scholar 

  13. Lieb, I.: Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudo convexen Gebieten: Stetige Randwerte. Math. Annalen199, 241–256 (1972)

    Google Scholar 

  14. Siu, Y. T.: The\(\bar \partial \) problem with uniform bounds on derivatives. Math. Annalen207, 163–176 (1974)

    Google Scholar 

  15. Stein, E. M.: Lectures on singular integrals and pseudodifferential operators. Princeton University Press (to appear)

  16. Stein, E. M.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press 1970

    Google Scholar 

  17. Stein, E. M.: Singular integrals and estimates for the Cauchy-Riemann equations. Bull. Amer. Math. Soc.79, 440–445 (1973)

    Google Scholar 

  18. Zygmund, A.: Trigometric series, second ed. Cambridge: Cambridge University Press 1968

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Much of the work in this paper is contained in the author's Princeton University Ph. D. Thesis. The author was supported by an NSF Graduate Fellowship during the writing of that thesis.

The author is grateful to E. M. Stein for suggesting this problem, and for his advice and encouragement during its solution.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krantz, S.G. Optimal Lipschitz andL p regularity for the equation\(\bar \partial u = f\) on strongly pseudo-convex domains. Math. Ann. 219, 233–260 (1976). https://doi.org/10.1007/BF01354286

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01354286

Navigation