Bulletin of the American Mathematical Society

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Book Information:

Author: R. Michael Range
Title: Holomorphic functions and integral representations in several complex variables
Additional book information: Graduate Texts in Mathematics, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1986, xi + 386 pp., $49.50. ISBN 0-387-96259-x.

Steven R. Bell, Biholomorphic mappings and the $\bar \partial$-problem, Ann. of Math. (2) 114 (1981), no. 1, 103–113. MR 625347, DOI 10.2307/1971379

Steve Bell and Ewa Ligocka, A simplification and extension of Fefferman’s theorem on biholomorphic mappings, Invent. Math. 57 (1980), no. 3, 283–289. MR 568937, DOI 10.1007/BF01418930

David Catlin, Necessary conditions for subellipticity and hypoellipticity for the $\bar \partial$-Neumann problem on pseudoconvex domains, Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979) Ann. of Math. Stud., vol. 100, Princeton Univ. Press, Princeton, N.J., 1981, pp. 93–100. MR 627751

David Catlin, Boundary invariants of pseudoconvex domains, Ann. of Math. (2) 120 (1984), no. 3, 529–586. MR 769163, DOI 10.2307/1971087

John P. D’Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. (2) 115 (1982), no. 3, 615–637. MR 657241, DOI 10.2307/2007015

Klas Diederich and John E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. of Math. (2) 107 (1978), no. 2, 371–384. MR 477153, DOI 10.2307/1971120

Klas Diederich and Peter Pflug, Necessary conditions for hypoellipticity of the $\bar \partial$-problem, Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979) Ann. of Math. Stud., vol. 100, Princeton Univ. Press, Princeton, N.J., 1981, pp. 151–154. MR 627755

Reinhold Remmert, Funktionentheorie. I, Grundwissen Mathematik [Basic Knowledge in Mathematics], vol. 5, Springer-Verlag, Berlin, 1984 (German). MR 753290, DOI 10.1007/978-3-642-96793-1

Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 350069, DOI 10.1007/BF01406845

Hans Grauert and Ingo Lieb, Das Ramirezsche Integral und die Lösung der Gleichung $\bar \partial f=\alpha$ im Bereich der beschränkten Formen, Rice Univ. Stud. 56 (1970), no. 2, 29–50 (1971) (German). MR 273057

H. Grauert and R. Remmert, Analytische Stellenalgebren, Die Grundlehren der mathematischen Wissenschaften, Band 176, Springer-Verlag, Berlin-New York, 1971 (German). Unter Mitarbeit von O. Riemenschneider. MR 0316742

Hans Grauert and Reinhold Remmert, Theory of Stein spaces, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 236, Springer-Verlag, Berlin-New York, 1979. Translated from the German by Alan Huckleberry. MR 580152

Hans Grauert and Reinhold Remmert, Coherent analytic sheaves, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 265, Springer-Verlag, Berlin, 1984. MR 755331, DOI 10.1007/978-3-642-69582-7

P. C. Greiner and E. M. Stein, Estimates for the $\overline \partial$-Neumann problem, Mathematical Notes, No. 19, Princeton University Press, Princeton, N.J., 1977. MR 0499319

G. M. Henkin, Integral representation of functions in strongly pseudoconvex regions, and applications to the $\overline \partial$-problem, Mat. Sb. (N.S.) 82 (124) (1970), 300–308 (Russian). MR 0265625

Lars Hörmander, $L^{2}$ estimates and existence theorems for the $\bar \partial$ operator, Acta Math. 113 (1965), 89–152. MR 179443, DOI 10.1007/BF02391775

Lars Hörmander, An introduction to complex analysis in several variables, 3rd ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990. MR 1045639

18.

A. Hurwitz and R. Courant, Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, 1. Aufl, Springer-Verlag, Berlin, 1922.

Klaus Jänich, Einführung in die Funktionentheorie, Hochschultext [University Textbooks], Springer-Verlag, Berlin-New York, 1977 (German). MR 0473147

20.

J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. I, Ann. of Math. (2) 78 (1963), 112-148; II, Ann. of Math. (2) 79 (1964), 450-472.

J. J. Kohn, Subellipticity of the $\bar \partial$-Neumann problem on pseudo-convex domains: sufficient conditions, Acta Math. 142 (1979), no. 1-2, 79–122. MR 512213, DOI 10.1007/BF02395058

J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443–492. MR 181815, DOI 10.1002/cpa.3160180305

J. J. Kohn and L. Nirenberg, A pseudo-convex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265–268. MR 330513, DOI 10.1007/BF01428194

Ingo Lieb, Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten. Beschränkte Lösungen, Math. Ann. 190 (1970/71), 6–44 (German). MR 283235, DOI 10.1007/BF01349966

Ingo Lieb and R. Michael Range, Integral representations and estimates in the theory of the $\overline \partial$-Neumann problem, Ann. of Math. (2) 123 (1986), no. 2, 265–301. MR 835763, DOI 10.2307/1971272

Enrique Ramírez de Arellano, Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis, Math. Ann. 184 (1969/70), 172–187 (German). MR 269874, DOI 10.1007/BF01351561

Reinhold Remmert, Funktionentheorie. I, Grundwissen Mathematik [Basic Knowledge in Mathematics], vol. 5, Springer-Verlag, Berlin, 1984 (German). MR 753290, DOI 10.1007/978-3-642-96793-1

S. M. Webster, Biholomorphic mappings and the Bergman kernel off the diagonal, Invent. Math. 51 (1979), no. 2, 155–169. MR 528021, DOI 10.1007/BF01390226

1.

S. R. Bell, Biholomorphic mappings and the $\bar \partial $-problem, Ann. of Math. (2) 114 (1980), 103-113. MR 0625347

2.

S. R. Belll and E. Ligocka, A simplification and extension of Fefferman's theorem in biholomorphic mappings, Invent. Math. 57 (1980), 283-289. MR 568937

3.

D. Catlin, Necessary conditions of subellipticity and hypoellipticity for the $\bar \partial $-Neumann problem on pseudoconvex domains, Recent Developments in Several Complex Variables, Ann. of Math. Studies no. 100, 1981. MR 627751

4.

D. Catlin, Boundary invariants of pseudoconvex domains, Ann. of Math. (2) 120 (1984), 529-586. MR 769163

5.

J. D'Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. (2) 115 (1982), 615-637. MR 657241

6.

K. Diederich and J. E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. of Math. (2) 107 (1978), 371-384. MR 477153

7.

K. Diederich and H. P. Pflug, Necessary conditions for hypoellipticity of the $\bar \partial $-problem, Recent Developments in Several Complex Variables, Ann. of Math. Studies no. 100, 1981, pp. 151-154. MR 627755

8.

K. Diederich and R. Remmert, Funktionentheorie. I, Springer-Verlag, Berlin-Heidelberg-New York, 1972. MR 753290

9.

C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. MR 350069

10.

H. Grauert and I. Lieb, Das Ramirezsche Integral und die Lösung der Gleichung $\bar \partial f=\alpha $ im Bereich der beschränkten Formen, Proc. Conf. Complex Analysis, Rice Univ., 1969, Rice Univ. Studies no. 56, 1970, pp. 29-50. MR 273057

11.

H. Grauert and R. Remmert, Analytische Stellenalgebren, Springer-Verlag, Berlin-Heidelberg-New York, 1971. MR 316742

12.

H. Grauert and R. Remmert, Theory of Stein spaces, Springer-Verlag, Berlin-Heidelberg, New York, 1979. MR 580152

13.

H. Grauert and R. Remmert, Coherent analytic sheaves, Springer-Verlag, Berlin-Heidelberg-New York, 1984. MR 755331

14.

P. C. Greiner and E. M. Stein, Estimates for the $øverline \partial $-Neumann problem, Princeton Univ. Press, Princeton, N.J., 1977. MR 499319

15.

G. M. Henkin, Integral representations of functions in strictly pseudoconvex domains and applications to the $øverline \partial $-problem, Math. Sb. 82 (1970), 300-308; English transl., Math. USSR Sb. 11 (1970), 273-281. MR 265625

16.

L. Hörmander, L, Acta Math. 113 (1965), 89-152. MR 179443

17.

L. Hörmander, An introduction to complex analysis in several variables, 2nd ed., North-Holland, Amsterdam-London, 1973. MR 1045639

18.

A. Hurwitz and R. Courant, Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, 1. Aufl, Springer-Verlag, Berlin, 1922.

19.

K. Jänich, Einführung in die Funktionentheorie, Springer-Verlag, Berlin-Heidelberg-New York, 1977. MR 473147

20.

J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. I, Ann. of Math. (2) 78 (1963), 112-148; II, Ann. of Math. (2) 79 (1964), 450-472.

21.

J. J. Kohn, Subellipticity of the $\bar \partial $-Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979), 79-122. MR 512213

22.

J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443-492. MR 181815

23.

J. J. Kohn and L. Nirenberg, A pseudoconvex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265-268. MR 330513

24.

I. Lieb, Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudo-konvexen Gebieten, Math. Ann. 190 (1970), 6-44. MR 283235

25.

I. Lieb and R. M. Range, Integral representations and estimates in the theory of the $øverline\partial$-Neumann problem, Ann. of Math. (2) 123 (1986), 265-301. MR 835763

26.

E. Ramirez, Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis, Math. Ann. 184 (1970), 172-187. MR 269874

27.

R. Remmert, Funktionentheorie. I, Grundwissen Mathematik no. 5, Springer-Verlag, Berlin-Heidelberg-New York, 1984. MR 753290

28.

S. Webster, Biholomorphic mappings and the Bergman kernel of the diagonal, Invent. Math. 51 (1979), 155-169. MR 528021