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Boundary regularity for the Cauchy-Riemann complex

  • I Séminaire d'Analyse (Paris)
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Séminaire Pierre Lelong-Henri Skoda (Analyse) Années 1980/81

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 919))

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References

  1. W. Fischer/I. Lieb. Lokale Kerne und beschränkte Lösungen für den \(\bar \partial\)-Operator auf q-konvexen Gebieten. Math. Ann. 208, 249–265 (1974)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  3. P. Greiner/E. Stein. Estimates for the \(\bar \partial\)-Neumann problem. Princeton 1977

    Google Scholar 

  4. G. M. Henkin. Integral representations of functions in strictly pseudoconvex domains and some applications. Mat. Sb. 78, 611–632 (1969). Maths USSR Sb. 7, 597–616 (1969)

    MathSciNet  Google Scholar 

  5. G. M. Henkin. Integral representations in strictly pseudoconvex domains and applications to the \(\bar \partial\)-problem. Mat. Sb. 82, 300–308 (1970). 273–281 (1970)

    MathSciNet  Google Scholar 

  6. G. M. Henkin/A. V. Romanov. Exact Hölder estimates for the solution of the \(\bar \partial\)-equation. Izv. Ak. Nauk USSR 35, 1171–1183 (1971). Maths. USSR Izv. 5, 1180–1192 (1971)

    MathSciNet  Google Scholar 

  7. M. Hortmann. Über die Lösbarkeit der \(\bar \partial\)-Gleichung mit Hilfe von Lp, Ck und D'-stetigen Integraloperatoren. Math. Ann. 223, 139–156 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  8. N. Kerzman. Hölder and Lp estimates for solutions of \(\bar \partial u = f\) in strongly pseudoconvex domains. Comm. Pure Appl. Math 24, 301–379 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  9. J. J. Kohn. Subellipticity of the \(\bar \partial\)-Neumann problem on pseudoconvex domains: sufficient conditions. Acta Math. 142, 79–122 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  10. J. J. Kohn/L. Nirenberg. A pseudoconvex domain not admitting a holomorphic support function. Math. Ann. 201, 265–268 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  11. I. Lieb. Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten. I. Math. Ann. 190, 6–44 (1970). II. Math. Ann. 199 241–256 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  12. I. Lieb. Beschränkte Lösungen der Cauchy-Riemannschen Differentialgleichungen auf q-konkaven Gebieten. Man. math. 26, 387–409 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  13. I. Lieb/R. M. Range. Lösungsoperatoren für den Cauchy-Riemann-Komplex mit Cκ-Abschätzungen. (1980 preprint)

    Google Scholar 

  14. E. Ramirez de A.. Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis. Math. Ann. 184, 172–187 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  15. R. M. Range. Hölder estimates for \(\bar \partial\) on convex domains in ℂ2 with real-analytic boundary. Proc. Symp. Pure Mathematics XXX, 2, 31–33 (1977)

    Article  Google Scholar 

  16. R. M. Range. On Hölder estimates for \(\bar \partial u = f\) on weakly pseudoconvex domains. Proc. Conf. Complex Anal. Cortona 1976–77, Sc. Norm. Sup. Pisa 1978

    Google Scholar 

  17. R. M. Range/Y. T. Siu. Uniform estimates for the \(\bar \partial\)-equation on domains with piecewise smooth strictly pseudoconvex boundaries. Math. Ann 206, 325–354 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  18. R. T. Seeley. Extension of C∞-functions defined in a half space. Proc. Amer. Math. Soc. 15, 625–626 (1964)

    MathSciNet  MATH  Google Scholar 

  19. N. Sibony. Un exemple de domaine pseudoconvexe régulier où l'équation \(\bar \partial = f\) n'admet pas de solution bornée pour f bornée. (1980 preprint)

    Google Scholar 

  20. Y. T. Siu. The \(\bar \partial\)-problem with uniform bounds on derivatives. Math. Ann. 207, 163–176 (1974)

    Article  MathSciNet  MATH  Google Scholar 

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Author notes

  1. R. Michael Range

    Present address: Department of Mathematics, SUNY at Albany, 12222, Albany, N. Y.

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    1. R. Michael Range
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    Pierre Lelong Henri Skoda

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    © 1982 Springer-Verlag

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    Range, R.M. (1982). Boundary regularity for the Cauchy-Riemann complex. In: Lelong, P., Skoda, H. (eds) Séminaire Pierre Lelong-Henri Skoda (Analyse) Années 1980/81. Lecture Notes in Mathematics, vol 919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097049

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    • DOI: https://doi.org/10.1007/BFb0097049

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-11482-6

    • Online ISBN: 978-3-540-39147-0

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