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

  • R. Michael Range
Special Year Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 1276)

Keywords

Heisenberg Group Pseudodifferential Operator Pseudoconvex Domain Approximate Symmetry Bergman Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Alt]
    Alt, W., Hölderabschätzungen für Ableitungen von Lösungen der Gleichung \(\bar \partial\) u=f bei streng pseudokonvexem Rand, Man. Math. 13(1974), 381–414.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [GrLi]
    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.MathSciNetzbMATHGoogle Scholar
  3. [GrSt]
    Greiner, P., and Stein, E.M., Estimates for the \(\bar \partial\)-Neumann Problem, Princeton University Press, 1977.Google Scholar
  4. [HaPo]
    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.MathSciNetzbMATHGoogle Scholar
  5. [Hen]
    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.MathSciNetGoogle Scholar
  6. [HeLe]
    Henkin, G.M., and Leiterer, J., Theory of Functions on Complex Manifolds. Birkhäuser, Boston, 1984Google Scholar
  7. [KeSt]
    Kerzman, N., and Stein, E.M., The Szegö kernel in terms of Cauchy-Fantappiè kernels, Duke Math. J. 45 (1978), 197–224.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [Koh 1]
    Kohn, J.J., Harmonic integrals on strongly pseudoconvex manifolds, I, Ann. of Math. 78(1963), 112–148, II, ibid. 79(1964), 450–472.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [Koh 2]
    _____, A survey of the \(\bar \partial\) -neumann Problem. Proc. Symp. Pure Math. 41, 137–145, Amer. Math. Soc., Providence, RI 1984.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [LiRa 1]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [LiRa 2]
    _____, Integral representations and estimates in the theory of the \(\bar \partial\) -Neumann problem. Ann. of Math. 123(1986), 265–301.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [LiRa 3]
    _____, Estimates for a class of integral operators and applications to the \(\bar \partial\) -Neumann problem, Invent. Math. 85(1986), 415–438.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [LiRa 4]
    _____, The kernel of the \(\bar \partial\) -Neumann operator on strictly pseudoconvex domains. (In preparation).Google Scholar
  14. [Lig]
    Ligocka, E. The Hölder continuity of the Bergman projection and proper holomorphic mappings, Studia Math. 80(1984), 89–107.MathSciNetzbMATHGoogle Scholar
  15. [Pho]
    Phong, D.H., On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. USA 76(1979), 1554–1558.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [PhSt]
    Phong, D.H., and Stein, E.M., Hilbert integrals, singular integrals, and Radon transforms I. Acta Math. (to appear).Google Scholar
  17. [Ran 1]
    Range, R.M., An elementary integral solution operator for the Cauchy-Riemann equations on pseudoconvex domains inn. Trans. Amer. Math. Soc. 274(1982), 809–816.MathSciNetzbMATHGoogle Scholar
  18. [Ran 2]
    _____, The \(\bar \partial\) -Neumann operator on the unit ball inn, Math. Ann 266(1984), 449–456.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [Ran 3]
    _____, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer-Verlag, New York, 1986.CrossRefzbMATHGoogle Scholar
  20. [Siu]
    Siu, Y.-T., The \(\bar \partial\) -problem with uniform bounds on derivatives, Math. Ann. 207(1974), 163–176.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • R. Michael Range
    • 1
  1. 1.Department of MathematicsState University of New York at AlbanyAlbany

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