Partially supported by NSF Grants MCS 83-00854 and DMS 85-01342.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alt, W., Hölderabschätzungen für Ableitungen von Lösungen der Gleichung \(\bar \partial\) u=f bei streng pseudokonvexem Rand, Man. Math. 13(1974), 381–414.
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.
Greiner, P., and Stein, E.M., Estimates for the \(\bar \partial\)-Neumann Problem, Princeton University Press, 1977.
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.
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.
Henkin, G.M., and Leiterer, J., Theory of Functions on Complex Manifolds. Birkhäuser, Boston, 1984
Kerzman, N., and Stein, E.M., The Szegö kernel in terms of Cauchy-Fantappiè kernels, Duke Math. J. 45 (1978), 197–224.
Kohn, J.J., Harmonic integrals on strongly pseudoconvex manifolds, I, Ann. of Math. 78(1963), 112–148, II, ibid. 79(1964), 450–472.
_____, A survey of the \(\bar \partial\) -neumann Problem. Proc. Symp. Pure Math. 41, 137–145, Amer. Math. Soc., Providence, RI 1984.
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.
_____, Integral representations and estimates in the theory of the \(\bar \partial\) -Neumann problem. Ann. of Math. 123(1986), 265–301.
_____, Estimates for a class of integral operators and applications to the \(\bar \partial\) -Neumann problem, Invent. Math. 85(1986), 415–438.
_____, The kernel of the \(\bar \partial\) -Neumann operator on strictly pseudoconvex domains. (In preparation).
Ligocka, E. The Hölder continuity of the Bergman projection and proper holomorphic mappings, Studia Math. 80(1984), 89–107.
Phong, D.H., On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. USA 76(1979), 1554–1558.
Phong, D.H., and Stein, E.M., Hilbert integrals, singular integrals, and Radon transforms I. Acta Math. (to appear).
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.
_____, The \(\bar \partial\) -Neumann operator on the unit ball in ℂn, Math. Ann 266(1984), 449–456.
_____, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer-Verlag, New York, 1986.
Siu, Y.-T., The \(\bar \partial\) -problem with uniform bounds on derivatives, Math. Ann. 207(1974), 163–176.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0078964
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18357-0
Online ISBN: 978-3-540-47904-8
eBook Packages: Springer Book Archive