×

Kernels for the tangential Cauchy-Riemann equations. (English) Zbl 0489.32014


MSC:

32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. Andreotti, C. Denson Hill, S. Łojasiewicz, and B. MacKichan, Complexes of differential operators. The Mayer-Vietoris sequence, Invent. Math. 35 (1976), 43 – 86. · Zbl 0332.58016 · doi:10.1007/BF01390133
[2] A. Boggess, Plemelj jump formulas for the fundamental solution to \( {\bar \partial _b}\) on the sphere, preprint.
[3] Jiri Dadok and Reese Harvey, The fundamental solution for the Kohn-Laplacian \?\?_{\?} on the sphere in \?\(^{n}\), Math. Ann. 244 (1979), no. 2, 89 – 104. · Zbl 0416.35067 · doi:10.1007/BF01420485
[4] G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Annals of Mathematics Studies, No. 75. · Zbl 0247.35093
[5] Hans Grauert and Ingo Lieb, Das Ramirezsche Integral und die Lösung der Gleichung \partial \?=\? im Bereich der beschränkten Formen, Rice Univ. Studies 56 (1970), no. 2, 29 – 50 (1971) (German). · Zbl 0217.39202
[6] R. Harvey and J. Polking, Fundamental solutions in complex analysis. I, II, Duke Math. J. 46 (1979), 253-300; 301-340. · Zbl 0441.35043
[7] G. M. Henkin, Integral representation of functions which are holomorphic in strictly pseudoconvex regions, and some applications, Mat. Sb. (N.S.) 78 (120) (1969), 611 – 632 (Russian).
[8] -, Integral representations of functions holomorphic in strictly pseudo-convex domains and applications to the \( \bar \partial \) problem, Mat. Sb. 82 (124) (1970), 300-308; English transl, in Math. USSR-Sb. 11 (1970), 273-281.
[9] G. M. Henkin, Solutions with bounds for the equations of H. Lewy and Poincaré-Lelong. Construction of functions of Nevanlinna class with given zeros in a strongly pseudoconvex domain, Dokl. Akad. Nauk SSSR 224 (1975), no. 4, 771 – 774 (Russian).
[10] -, The H. Lewy equation and analysis of pseudo-convex manifolds, Uspehi Mat. Nauk 32 (1977), no. 3; English transl, in Russian Math. Surveys 32 (1977).
[11] -, H. Lewy’s equation and analysis on a pseudo-convex manifolds. II, Mat. Sb. 102 (144) (1977), 71-108; English transl. in Math. USSR-Sb. 31 (1977), 63-94.
[12] L. Hörmander, An introduction to complex analysis in several variables, Van Nostrand, Princeton, N. J., 1965. · Zbl 0138.06203
[13] L. R. Hunt, J. C. Polking, and M. J. Strauss, Unique continuation for solutions to the induced Cauchy-Riemann equations, J. Differential Equations 23 (1977), no. 3, 436 – 447. · Zbl 0337.35001 · doi:10.1016/0022-0396(77)90121-8
[14] Nils Øvrelid, Integral representation formulas and \?^{\?}-estimates for the \partial -equation, Math. Scand. 29 (1971), 137 – 160. · Zbl 0227.35069 · doi:10.7146/math.scand.a-11041
[15] Enrique Ramírez de Arellano, Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis, Math. Ann. 184 (1969/1970), 172 – 187 (German). · Zbl 0189.09702 · doi:10.1007/BF01351561
[16] A. V. Romanov, A formula and estimates for the solution of the tangential Cauchy-Riemann equation, Dokl. Akad. Nauk SSSR 220 (1975), 532 – 535 (Russian).
[17] A. V. Romanov, A formula and estimates for the solutions of the tangential Cauchy-Riemann equation, Mat. Sb. (N.S.) 99(141) (1976), no. 1, 58 – 83, 135 (Russian). · Zbl 0338.35066
[18] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. · Zbl 0207.13501
[19] R. O. Wells Jr., Compact real submanifolds of a complex manifold with nondegenerate holomorphic tangent bundles, Math. Ann. 179 (1969), 123 – 129. · Zbl 0167.21604 · doi:10.1007/BF01350124
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.