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Integral representations in the theory of the \(\bar \partial\)-Neumann problem

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Complex Analysis II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1276))

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Partially supported by NSF Grants MCS 83-00854 and DMS 85-01342.

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References

  1. Alt, W., Hölderabschätzungen für Ableitungen von Lösungen der Gleichung \(\bar \partial\) u=f bei streng pseudokonvexem Rand, Man. Math. 13(1974), 381–414.

    Article  MathSciNet  MATH  Google Scholar 

  2. Grauert, H., and Lieb, I., Das Ramirezsche Integral und die Lösung der Gleichung \(\bar \partial\) f=α im Bereich der beschränkten Formen, Rice Univ. Studies 56(1970), 29–50.

    MathSciNet  MATH  Google Scholar 

  3. Greiner, P., and Stein, E.M., Estimates for the \(\bar \partial\)-Neumann Problem, Princeton University Press, 1977.

    Google Scholar 

  4. Harvey, R., and Polking, J., The \(\bar \partial\) -Neumann solution to the inhomogeneous Cauchy-Riemann equations in the ball in ℂ n, Trans. AMS 281(1984), 587–613.

    MathSciNet  MATH  Google Scholar 

  5. Henkin, G.M., Integral representations in strictly pseudoconvex domains and applications to the \(\bar \partial\) -problem, Mat. Sb. 82(1970), 300–308; Math. USSR Sb. 11(1970), 273–281.

    MathSciNet  Google Scholar 

  6. Henkin, G.M., and Leiterer, J., Theory of Functions on Complex Manifolds. Birkhäuser, Boston, 1984

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Kohn, J.J., Harmonic integrals on strongly pseudoconvex manifolds, I, Ann. of Math. 78(1963), 112–148, II, ibid. 79(1964), 450–472.

    Article  MathSciNet  MATH  Google Scholar 

  9. _____, A survey of the \(\bar \partial\) -neumann Problem. Proc. Symp. Pure Math. 41, 137–145, Amer. Math. Soc., Providence, RI 1984.

    Article  MathSciNet  MATH  Google Scholar 

  10. Lieb, I., and Range, R.M., On integral representations and a priori Lipschitz estimates for the canonical solution of the \(\bar \partial\) -equation, Math. Ann. 265(1983), 221–251.

    Article  MathSciNet  MATH  Google Scholar 

  11. _____, Integral representations and estimates in the theory of the \(\bar \partial\) -Neumann problem. Ann. of Math. 123(1986), 265–301.

    Article  MathSciNet  MATH  Google Scholar 

  12. _____, Estimates for a class of integral operators and applications to the \(\bar \partial\) -Neumann problem, Invent. Math. 85(1986), 415–438.

    Article  MathSciNet  MATH  Google Scholar 

  13. _____, The kernel of the \(\bar \partial\) -Neumann operator on strictly pseudoconvex domains. (In preparation).

    Google Scholar 

  14. Ligocka, E. The Hölder continuity of the Bergman projection and proper holomorphic mappings, Studia Math. 80(1984), 89–107.

    MathSciNet  MATH  Google Scholar 

  15. Phong, D.H., On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. USA 76(1979), 1554–1558.

    Article  MathSciNet  MATH  Google Scholar 

  16. Phong, D.H., and Stein, E.M., Hilbert integrals, singular integrals, and Radon transforms I. Acta Math. (to appear).

    Google Scholar 

  17. Range, R.M., An elementary integral solution operator for the Cauchy-Riemann equations on pseudoconvex domains in ℂn. Trans. Amer. Math. Soc. 274(1982), 809–816.

    MathSciNet  MATH  Google Scholar 

  18. _____, The \(\bar \partial\) -Neumann operator on the unit ball in ℂn, Math. Ann 266(1984), 449–456.

    Article  MathSciNet  MATH  Google Scholar 

  19. _____, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer-Verlag, New York, 1986.

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Carlos A. Berenstein

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© 1987 Springer-Verlag

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Range, R.M. (1987). Integral representations in the theory of the \(\bar \partial\)-Neumann problem. In: Berenstein, C.A. (eds) Complex Analysis II. Lecture Notes in Mathematics, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078964

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  • DOI: https://doi.org/10.1007/BFb0078964

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18357-0

  • Online ISBN: 978-3-540-47904-8

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