Skip to main content
SpringerLink
Log in

Hölder andL p-estimates for the ∂ equation in some convex domains with real-analytic boundary

  • 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Grauert, H., Lieb, I.: Das Ramirezsche Integral und die Lösung der Gleichung\(\bar \partial f = \alpha \) im Bereich der beschränkten Formen. Rice Univ. Stud.56, 26–50 (1970)

    Google Scholar 

  2. Henkin, G.M.: Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications. Math. USSR Sb.11, 273–281 (1970)

    Google Scholar 

  3. Henkin, G.M., Romanov, A.V.: Exact Hölder estimates for the solutions of the\(\bar \partial \)-equation Math. USSR Izv.5, 1180–1192 (1971)

    Google Scholar 

  4. Kerzman, N., Stein, E.M.: The Szegö kernel in terms of Cauchy-Fantappré kernels. Duke Math. J.45, 197–224 (1978)

    Google Scholar 

  5. Lieb, I.: Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten. Math. Ann.190, 6–44 (1970)

    Google Scholar 

  6. Milnor, J.: Singular points of complex hypersurfaces. Annals of Mathematical Studies. Princeton N.J.: Princeton University Press 1968

    Google Scholar 

  7. Ramirez de Arellano, E.: Ein Divisionproblem und Randintegraldarstellungen in der komplexen Analysis. Math. Ann.184, 172–187 (1970)

    Google Scholar 

  8. Range, R.M.: On Hölder estimates for\(\bar \partial u = f\) on weakly pseudoconvex domains. Proc. Int. Conf. Cortona, Italy 1976–77, 247–267 (1978)

  9. Range, R.M.: An elementary integral solution operator for the Cauchy-Riemann equations on pseudoconvex domains inC n. Trans. Am. Math. Soc.274, 809–816 (1982)

    Google Scholar 

  10. Rudin, W.: Function theory in the unit ball ofC n. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  11. Teissier, B.: Théorèmes de finitude en géométrie analytique. Séminaire Bourbaki, Vol. 1973/74. In: Lecture Notes in Mathematics, Vol. 431. Berlin, Heidelberg, New York: Springer 1975

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Secció de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain

    Joaquim Bruna & Joan del Castillo

Authors
  1. Joaquim Bruna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joan del Castillo
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper contains some results obtained in the Ph.D. thesis of the second author, read at the Universitat Autònoma de Barcelona

Partially supported by a grant of the Comisión Asesora de Investigación Científica y Técnica, Ministerio de Educación y Ciencia, Madrid

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bruna, J., del Castillo, J. Hölder andL p-estimates for the ∂ equation in some convex domains with real-analytic boundary. Math. Ann. 269, 527–539 (1984). https://doi.org/10.1007/BF01450763

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01450763

Keywords

Search

Navigation