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Integral representations on Hermitian manifolds: the $\bar \partial $-Neumann solution of the Cauchy-Riemann equations
Author(s):
Ingo
Lieb;
R. Michael
Range
Journal:
Bull. Amer. Math. Soc.
11
(1984),
355-358.
MSC (1980):
Primary 32A25, 32F20, 35N15;
Secondary 53C55
MathSciNet review:
752797
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Additional information
References:
- 1.
- G. de Rham, Variétés différentiables, Hermann, Paris, 1960.
- 2.
- P. Greiner and E. M. Stein, Estimates for the ā-Neumann problem, Princeton Univ. Press, Princeton, N.J., 1977. MR 499319
- 3.
- R. Harvey and J. Polking, The ā-Neumann solution to the inhomogeneous Cauchy-Riemann equation in the ball in C, Trans. Amer. Math. Soc. 281 (1984), 587-613. MR 722764
- 4.
- N. Kerzman and E. M. Stein, The Szegö kernel in terms of Cauchy-Fantappié kernels, Duke Math. J. 45 (1978), 197-224. MR 508154
- 5.
- J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. I, II, Ann. of Math. (2) 78 (1963), 112-148; ibid. 79 (1964), 450-472.
- 6.
- J. J. Kohn, Subellipticity of the ā-Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979), 79-122. MR 512213
- 7.
- I. Lieb and R. M. Range, On integral representations and a priori Lipschitz estimates for the canonical solution of ā, Math. Ann. 265 (1983), 221-251. MR 719137
- 8.
- E. Ligocka, The Hölder continuity of the Bergman projection and proper holomorphic mappings, 1983 (preprint). MR 781328
- 9.
- N. Øvrelid, Pseudodifferential operators and the ā-equation, Lecture Notes in Math., vol. 512, Springer-Verlag, 1976, pp. 185-192. MR 499321
- 10.
- D. H. Phong, On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. U.S.A. 76 (1979), 1554-1558. MR 526179
- 11.
- R. M. Range, The ā-Neumann operator on the unit ball in C, Math. Ann. 266 (1984), 449-456. MR 735527
- 12.
- N. K. Stanton, The solution of the ā-Neumann problem in a strictly pseudoconvex Siegel domain, Invent. Math. 65 (1981), 137-174. MR 636884
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Additional Information:
DOI:
10.1090/S0273-0979-1984-15305-9
PII:
S 0273-0979(1984)15305-9
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