Comptes Rendus
no. 11
Complex Analysis
A new characterization of a class of pseudoconvex domains in C2
[Une nouvelle caractérisation d'une classe des domaines pseudoconvexes en C2]

Présenté par : Jean-Pierre Demailly

Fabrizio Colombo1 ; M. Elena Luna-Elizarrarás2 ; Irene Sabadini1 ; Michael Shapiro2 ; Daniele C. Struppa3
1 Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy
2 Departamento de Matemáticas E.S.F.M. del I.P.N. 07338 México D.F., Mexico
3 Department of Mathematics and Computer Science, Chapman University, 92866 Orange, CA, USA
Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 677-680.

En utilisant l'inverse à droite de l'opérateur de Cauchy–Fueter, nous démontrons une caractérisation en forme intégrale d'une classe de domaines pseudoconvexes en C2.

By using the right inverse of the Cauchy–Fueter operator we obtain an explicit integral characterization of a class of pseudoconvex domains in C2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.04.014
Fabrizio Colombo 1 ; M. Elena Luna-Elizarrarás 2 ; Irene Sabadini 1 ; Michael Shapiro 2 ; Daniele C. Struppa 3

1 Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy
2 Departamento de Matemáticas E.S.F.M. del I.P.N. 07338 México D.F., Mexico
3 Department of Mathematics and Computer Science, Chapman University, 92866 Orange, CA, USA 
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     title = {A new characterization of a class of pseudoconvex domains in $ {\mathbb{C}}^{2}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {677--680},
     publisher = {Elsevier},
     volume = {344},
     number = {11},
     year = {2007},
     doi = {10.1016/j.crma.2007.04.014},
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Fabrizio Colombo; M. Elena Luna-Elizarrarás; Irene Sabadini; Michael Shapiro; Daniele C. Struppa. A new characterization of a class of pseudoconvex domains in $ {\mathbb{C}}^{2}$. Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 677-680. doi : 10.1016/j.crma.2007.04.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.04.014/

[1] F. Colombo; I. Sabadini; F. Sommen; D.C. Struppa Analysis of Dirac Systems and Computational Algebra, Progress in Mathematical Physics, vol. 39, Birkhäuser, Boston, 2004

[2] R. Fueter Über einen Hartogs'schen Satz, Comm. Math. Helv., Volume 12 (1939), pp. 75-80

[3] S. Krantz Function Theory of Several Complex Variables, John Wiley & Sons, New York, 1982

[4] I. Mitelman; M.V. Shapiro Differentiation of the Martinelli–Bochner integrals and the notion of hyperderivability, Math. Nachr., Volume 172 (1995), pp. 211-238

[5] K. Nôno Characterization of domains of holomorphy by the existence of hyper-conjugate harmonic functions, Rev. Roum. Math. Pures Appl., Volume 31 (1986), pp. 159-161

[6] J. Ryan Complex Clifford analysis and domains of holomorphy, J. Austral. Math. Soc. Ser. A, Volume 48 (1990), pp. 413-433

[7] M. Shapiro; N. Vasilevski On the Bergman kernel function in hypercomplex analysis, Acta Appl. Math., Volume 46 (1997), pp. 1-27

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