References
Andreotti, A., Vesentini, E.: Carleman estimates for the Laplace-Beltrami equation on complex manifolds. Publ. Math. Inst. Hautes Etud. Sci.25, 81–130 (1965)
Belanger, J.: Hölder estimates for\(\bar \partial\) inℂ 2. Thesis, Princeton Univ. 1987
Berndtsson, B., Andersson, M.: Henkin-Ramirez formulas with weight factors. Ann. Inst. Fourier32, 91–110 (1982)
Bonami, A., Charpentier, Ph.: Solutions de l'équation\(\bar \partial\) et zéros de la classe de Nevanlinna dans certains domaines faiblement pseudoconvexes. Ann. Inst Fourier32, 53–90 (1982)
Bonneau, P.: L'equation\(\bar \partial\) dans certains domaines faiblement convexes. Ann. Fac. Sci. Toulouse, V Ser., Math.7, 185–203 (1985)
Bonneau, P.: Solutions integrales de l'equation\(\bar \partial\) dans certains domaines pseudoconvexes sans fonction support holomorphe. C. R. Acad. Sci. Paris, Ser.304, 47–50 (1987)
Bonneau, P.: Solutions intégrales de l'opérateur de Cauchy-Riemann dans les domaines pseudoconvexes. Applications à des problèmes de division. Thèse d'Etat Univ. P. Sabatier Toulouse (1987)
Bruna, J., del Castillo, J.: Hölder andL p-estimates in some convex domains with real-analytic boundary. Math. Ann.269, 527–539 (1984)
Chang, D.C, Nagel, A., Stein, E.M.: Estimates for the\(\bar \partial\)-Neumann problem for pseudoconvex domains inℂ 2 of finite type. Proc. Natl. Acad. Sci. USA. To appear 1990
Christ, M.: Regularity properties of the\(\bar \partial\) equation on weakly pseudoconvexCR manifolds of dimension 3. J. Am. Math. Soc.1, 587–646 (1988)
Diederich, K., Fornaess, J.E.: Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions. Invent. Math.39, 129–141 (1977)
Diederich, K., Fornaess, J.E.: Proper holomorphic maps onto pseudoconvex domains with real-analytic boundary. Ann. Math.110, 575–592 (1979)
Diederich, K., Fornaess, J.E., Wiegerinck, J.: Sharp Hölder estimates for\(\bar \partial\) on ellipsoids. Manuscr. Math.56, 399–417 (1986)
Diederich, K., Herbort, G., Ohsawa, T.: The Bergman kernel on uniformly extendable pseudoconvex domains. Math. Ann.273, 471–478 (1986)
Diederich, K., Herbort, G.: Extension of holomorphic functions with growth conditions. Preprint 1989
Fefferman, Ch., Kohn, J.J.: Hölder estimates on domains of complex dimension two and on three dimensionalCR manifolds. Adv. Math.69, 223–303 (1988)
Fischer, W., Lieb, I.: Lokale Kerne und beschränkte Lösungen für den\(\bar \partial\)-Operator auf q-konvexen Gebieten. Math. Ann.208, 249–265 (1974)
Fornaess, J.E.: Peak points on weakly pseudoconvex domains. Math. Ann.227, 173–175 (1977)
Fornaess, J.E.: Sup-norm estimates for\(\bar \partial\) inℂ. Ann. Math.123, 335–345 (1986)
Fornaess, J.E., Sibony, N.: Oral communication about recent work
Grauert, H., Lieb, I.: Das Ramirezsche Integral und die Gleichung\(\bar \partial\) u =f im Bereich der beschränkten Formen. Rice Univ. Studies56, 29–50 (1970)
Henkin, G.M.: Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications. Math. USSR Sb.11, 273–282 (1970)
Hörmander, L.: An introduction to complex analysis in several variables. Amsterdam: North-Holland 1973
Kerzman, N.: Hölder andL p-estimates for solutions of\(\bar \partial\) u =f in strongly pseudoconvex domains. Commun. Pure Appl. Math.24, 301–379 (1971)
Kohn, J.J., Nirenberg, L.: A pseudoconvex domain not admitting a holomorphic support function. Math. Ann.201, 265–268 (1973)
Krantz, S.: Optimal Lipschitz- andL p-regularity for the equation\(\bar \partial\) u =f on strongly pseudoconvex domains. Math. Ann.219, 233–260 (1976)
Lieb, I.: Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten: Beschränkte Lösungen. Math. Ann.190, 6–44 (1970)
Ohsawa, T.: Boundary behavior of the Bergman kernel function on pseudoconvex domains. Publ. RIMS Kyoto20, 897–902 (1984)
Ohsawa, T., Takegoshi, K.: On the extension ofL 2-holomorphic functions. Math. Z.195, 197–204 (1987)
Øvrelid, N.: Integral representation formulas andL p-estimates for the\(\bar \partial\)-equation. Math. Scand.29, 137–160 (1971)
Ramirez de Arellano, E.: Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis. Math. Ann.184, 172–187 (1970)
Range, R.M.: On Hölder estimates for\(\bar \partial\) u =f on weakly pseudoconvex domains. Proc. In. Conf. Cortona, Italy 1976–1977. Sc. Norm. Sup. Pisa, 247–267 (1978)
Sibony, N.: Un exemple de domaine pseudoconvexe régulier où l'équation\(\bar \partial\) u =f n'admet pas de solution bornée pourf bornée. Invent. Math.62, 235–242 (1980)
Verdera, J.:L ∞-continuity of Henkin operators solving\(\bar \partial\) in certain weakly pseudoconvex domains ofℂ. Proc. R. Soc. Edinb. Sect. A99, 25–33 (1984)
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Dedicated to H. Grauert, on the occasion of his sixtieth birthday
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Bonneau, P., Diederich, K. Integral solution operators for the Cauchy-Riemann equations on pseudoconvex domains. Math. Ann. 286, 77–100 (1990). https://doi.org/10.1007/BF01453566
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DOI: https://doi.org/10.1007/BF01453566