Bulletin of the American Mathematical Society

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Book Information:

Author: Robert C. Gunning
Title: Introduction to holomorphic functions of several variables
Additional book information: Wadsworth & Brooks/Cole, vol. 1, Function theory, 202 pp. ISBN 0-534-13308-8; vol. 2, Local theory, 215 pp. ISBN 0-534-13309-6; vol. 3, Homological theory, 194 pp. ISBN 0-534-13310-X.

Aldo Andreotti and Edoardo Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 81–130. MR 175148

Eric Bedford and John Erik Fornæss, Counterexamples to regularity for the complex Monge-Ampère equation, Invent. Math. 50 (1978/79), no. 2, 129–134. MR 517774, DOI 10.1007/BF01390286

[BET] H. Behuke and P. Thullen, Theorie der funktionen mehrerer komplexer veränderlichen, Springer-Verlag, Berlin, 1934.

[BER] L. Bers, Introduction to several complex variables, New York Univ. Press, New York, 1964.

Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863

E. M. Čirka, The Lindelöf and Fatou theorems in $\textbf {C}^{n}$, Mat. Sb. (N.S.) 92(134) (1973), 622–644, 648 (Russian). MR 0338415

Michael Commichau and Hans Grauert, Das formale Prinzip für kompakte komplexe Untermannigfaltigkeiten mit $1$-positivem Normalenbündel, 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. 101–126 (German). MR 627752

[JPDA] J. D'Angelo, Finite-type conditions for real hypersurfaces in Cⁿ, (S. G. Krantz, ed.), Lecture Notes in Math., vol. 168, Springer-Verlag, Berlin, 1987, pp. 83-102.

Klas Diederich and John Erik Fornaess, Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), no. 2, 129–141. MR 437806, DOI 10.1007/BF01390105

Klas Diederich and John Erik Fornaess, Pseudoconvex domains: an example with nontrivial Nebenhülle, Math. Ann. 225 (1977), no. 3, 275–292. MR 430315, DOI 10.1007/BF01425243

Mike J. Field, Several complex variables and complex manifolds. I, London Mathematical Society Lecture Note Series, vol. 65, Cambridge University Press, Cambridge-New York, 1982. MR 651517

G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, No. 75, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588

G. B. Folland and E. M. Stein, Estimates for the $\bar \partial _{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 367477, DOI 10.1002/cpa.3160270403

John Erik Fornæss and Berit Stensønes, Lectures on counterexamples in several complex variables, Mathematical Notes, vol. 33, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1987. MR 895821

H. Grauert and K. Fritzsche, Several complex variables, Graduate Texts in Mathematics, Vol. 38, Springer-Verlag, New York-Heidelberg, 1976. Translated from the German. MR 0414912

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

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

Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696

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). MR 0249660

M. Hervé, Several complex variables. Local theory, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1963. MR 0151632

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, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075

[KOW] S. Kobayashi and H. H. Wu, Complex analytic geometry, Birkhäuser, Boston, 1983.

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

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

Steven G. Krantz, Function theory of several complex variables, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1982. MR 635928

[OSG] W. F. Osgood, Lehrbuch der Funktionenetheorie, II, Teubner, Leipzig, 1924.

Nils Øvrelid, Integral representation formulas and $L^{p}$-estimates for the $\bar \partial$-equation, Math. Scand. 29 (1971), 137–160. MR 324073, DOI 10.7146/math.scand.a-11041

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

R. Michael Range, Holomorphic functions and integral representations in several complex variables, Graduate Texts in Mathematics, vol. 108, Springer-Verlag, New York, 1986. MR 847923, DOI 10.1007/978-1-4757-1918-5

R. Michael Range, An elementary integral solution operator for the Cauchy-Riemann equations on pseudoconvex domains in $\textbf {C}^{n}$, Trans. Amer. Math. Soc. 274 (1982), no. 2, 809–816. MR 675081, DOI 10.1090/S0002-9947-1982-0675081-4

H. L. Royden, Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 369–383. MR 0288254

Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841

Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594

Nessim Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), no. 3, 205–230 (French). MR 385164, DOI 10.1007/BF01389850

E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Mathematical Notes, No. 11, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0473215

E. M. Stein, Singular integrals and estimates for the Cauchy-Riemann equations, Bull. Amer. Math. Soc. 79 (1973), 440–445. MR 315302, DOI 10.1090/S0002-9904-1973-13205-7

John Wermer, Banach algebras and several complex variables, 2nd ed., Graduate Texts in Mathematics, No. 35, Springer-Verlag, New York-Heidelberg, 1976. MR 0394218

[ANV] A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equations on complex manifolds, Publ. Math. Inst. Hautes Études Sci. 25 (1965), 81-130. MR 0175148




[BEF] E. Bedford and J. E. Fornaess, Counterexamples to regularity for the complex Monge-Ampère equation, Invent. Math. 50 (1979), 129-134. MR 517774




[BET] H. Behuke and P. Thullen, Theorie der funktionen mehrerer komplexer veränderlichen, Springer-Verlag, Berlin, 1934.




[BER] L. Bers, Introduction to several complex variables, New York Univ. Press, New York, 1964.




[BOM] S. Bochner and W. T. Martin, Several complex variables, Princeton Univ. Press, Princeton, NJ, 1948. MR 27863




[CIR] E. Cirka, The theorems of Lindelöf and Fatou in Cⁿ, Mat. Sb. 92 (134) (1973), 622-644; Math. U. S. S. R. Sb. 21 (1973), 619-639. MR 338415




[COG] M. Commichau and H. Grauert, Das formale Princip für kompakte komplexe Untermannigfaltigkeiten mit 1-positive Normalenbüdel, Recent Developments in Several Complex Variables (J. E. Fornaess, ed. ), Ann. of Math. Studies, vol. 100, Princeton Univ. Press, Princeton, NJ, 1981. MR 627752




[JPDA] J. D'Angelo, Finite-type conditions for real hypersurfaces in Cⁿ, (S. G. Krantz, ed.), Lecture Notes in Math., vol. 168, Springer-Verlag, Berlin, 1987, pp. 83-102.




[DIF1] K. Diederich and J. E. Fornaess, Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), 129-141. MR 437806




[DIF2] K. Diederich and J. E. Fornaess, Pseudoconvex domains: An example with nontrivial Nebenhülle, Math. Ann. 225 (1977), 275-292. MR 430315




[FIE] M. Field, Several complex variables and complex manifolds, Cambridge Univ. Press, Cambridge, 1982. MR 651517




[FOK] G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Princeton Univ. Press, Princeton, NJ, 1972. MR 461588




[FOS] G. B. Folland and E. M. Stein, Estimates for the $\bar \partial \sbb$ complex and analysis of the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522. MR 367477




[FRS] J. E. Fornaess and B. Stensones, Lectures on counterexamples in several complex variables, Princeton Univ. Press, Princeton, NJ, 1987. MR 895821




[GRF] H. Grauert and K. Fritzsche, Several complex variables, Springer-Verlag, Berlin, 1976. MR 414912




[GRL] H. Grauert and I. Lieb, Das Ramirezsche Integral und die Lösung der Gleichung $\bar \partial f=\alpha $ im Bereich der beschränkten Formen, Complex Analysis (Proc. Conf., Rice Univ., Houston, Tex., 1969), Rice Univ. Studies 56 (1970), no. 2, (1971), 29-50. MR 273057




[GRR1] H. Grauert and R. Remmert, Theory of Stein spaces, Springer-Verlag, Berlin, 1979. MR 580152




[GRR2] H. Grauert and R. Remmert, Coherent analytic sheaves, Springer-Verlag, Berlin, 1984. MR 755331




[GUR] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, Englewood Cliffs, NJ, 1965. MR 180696




[HEN] G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications, Mat. Sb. 78 (120) (1969), 611-632; Math. U. S. S. R. Sb. 11 (1970), 273-281. MR 249660




[HER] M. Hervé, Several complex variables: Local theory, Oxford Univ. Press, Oxford, 1963. MR 151632




[HOR1] L. Hörmander, L, Acta Math. 113 (1965), 89-152. MR 179443




[HOR2] L. Hörmander, Introduction to complex analysis in several variables, Van Nostrand, Princeton, NJ, 1967. MR 203075




[KOW] S. Kobayashi and H. H. Wu, Complex analytic geometry, Birkhäuser, Boston, 1983.




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




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




[KRA] S. G. Krantz, Function theory of several complex variables, John Wiley and Sons, New York, 1982. MR 635928




[OSG] W. F. Osgood, Lehrbuch der Funktionenetheorie, II, Teubner, Leipzig, 1924.




[OVR] N. Øvrelid, Integral representation formulas and $L\spp$-estimates for the $\bar \partial $-equation, Math. Scand. 29 (1971), 137-160. MR 324073




[RAM] E. Ramirez, Divisions problem in der komplexen analysis mit einer Anwendung auf Rand integral darstellung, Math. Ann. 184 (1970), 172-187. MR 269874




[RAN1] R. M. Range, Holomorphic functions and integral representations in several complex variables, Springer-Verlag, Berlin, 1986. MR 847923




[RAN2] R. M. Range, An elementary integral solution operator for the Cauchy-Riemann equations on pseudoconvex domains in Cⁿ, Trans. Amer. Math. Soc. 274 (1982), 809-816. MR 675081




[ROY] H. Royden, Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, NY, 1969), Annals of Math. Studies 66, Princeton Univ. Press, Princeton, NJ, 1971, pp. 369-383. MR 288254




[RUD1] W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 255841




[RUD2] W. Rudin, Function theory in the unit ball of Cⁿ, Springer-Verlag, Berlin, 1980. MR 601594




[SIB] N. Sibony, Prolongement des fonctions holomorphies bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230. MR 385164




[STE1] E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Princeton Univ. Press, Princeton, NJ, 1972. MR 473215




[STE2] E. M. Stein, Singular integrals and estimates for the Cauchy-Riemann equations, Bull. Amer. Math. Soc. 79 (1973), 440-445. MR 315302




[WER] J. Wermer, Banach algebra and several complex variables, Springer-Verlag, Berlin, 1976.s MR 394218