Abstract
In this paper, we discuss the relations between a special Heisenberg coordinate system and a normalized Levi metric on strongly pseudo-convex domains in Cn and see how they are related to the\(\bar \partial \)-Neumann operator.
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Beals, M., Fefferman, C., Grossman, R.: Strictly pseudo-convex domains in ℂn, Bulletin AMS, (New series)8 125–322 (1983)
Beals, R., Greiner, P.C., Stanton, N.: Lp and Lipschitz estimates for the\(\bar \partial \)-equation and the\(\bar \partial \)-Neumann problem, to appear in Math Annalen, (1987)
Chang, D.C.: Optimal Hölder and Lp regularity for the Kohn solution of the\(\bar \partial \)-equation on strongly pseudo-convex domains, Transaction of the AMS, to appear
Chang, D.C.: On Lp and Hölder estimates for the\(\bar \partial \)-Neumann problem on strongly pseudoconvex domain, Math. Annalen, to appear
Fefferman, C.L.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Inventiones Math.,26, 1–66 (1974)
Folland, G.B., Kohn, J.J.: The Neumann problem for the Cauchy-Riemann complex, Ann. of math. Study #75, Princeton Univ. Press, Princeton, NJ., 1972
Folland, G.B., Stein, E.M.: Estimates for the\(\overline {\partial _b } \) complex and analysis on the Heisenberg group, Comm. Pure & Applied Math.27, 429–522 (1974)
Greiner, P.C., Stein, E.M.: Estimates for the\(\bar \partial \)-Neumann problem, Math. Notes #19, Princeton Univ. Press, Princeton, N.J., 1977
Kerzman, N.: Singular integrals in complex analysis, Proc. of Symposia in Pure Math.,35, 3–41 (1979)
Kohn, J.J., Rossi, H.: On the extension of holomorphic functions from the boundary of a complex manifold, Ann. of Math.,81, 451–472 (1965)
Krantz, S.G.: Function theory of several complex variables, Wiley, New York,1982
Lieb, I., Range, R.M.: On integral representations and a prioi Lipschitz estimates for the canonical solution of the\(\bar \partial \)-equations, Math. Annalen,265, 221–251 (1983)
Lieb, I., Range, R.M.: Integral representations and estimates in the theory of the\(\bar \partial \)-Neumann problem, Ann. of Math,123, 265–301 (1986)
Lieb, I., Range, R.M.: The kernel of the\(\bar \partial \)-Neumann operator on strictly pseudo-convex domains, Math. Annalen,278, 151–173 (1986)
Phong, D.H.: On integral representations of the\(\bar \partial \)-Neumann operator, Proc. Nat. Acad. Sci. USA76, 1554–1558 (1979)
Phong, D.H., Stein, E.M.: Hilbert integrals, singular integrals and Radon transforms I, Acta Math.157, 99–157 (1986)
Phong, D.H., Stein, E.M.: Hilbert integrals, singular integrals and Radon transforms II, Inventions Math,86, 75–113 (1986)
Rothschild, L.P., Stein, E.M.: Hypoelliptic differential operators and nilpotent gronps, Acta Math.137, 247–320 (1976)
Stein, E.M.: Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ.,1970
Stein, E.M.: Singular integral operators and nilpotent groups, C.I.M.E. Roma, 148–206 (1975)
Stein, E.M.: Lecture notes on the Heisenberg group, Preprint (1983)
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Work supported by MSRI, Berkeley, California.
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Chang, DC.E. A note on the kernel of the\(\bar \partial \)-Neumann operator on strongly pseudo-convex domains. Manuscripta Math 62, 437–447 (1988). https://doi.org/10.1007/BF01357720
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DOI: https://doi.org/10.1007/BF01357720