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
Colombo, Fabrizio1 ; Luna-Elizarrarás, M. Elena2 ; Sabadini, Irene1 ; Shapiro, Michael2 ; Struppa, Daniele C.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
Comptes Rendus. Mathématique, Tome 344 (2007) no. 11, pp. 677-680

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

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.04.014

Colombo, Fabrizio 1 ; Luna-Elizarrarás, M. Elena 2 ; Sabadini, Irene 1 ; Shapiro, Michael 2 ; Struppa, Daniele C. 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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Colombo, Fabrizio; Luna-Elizarrarás, M. Elena; Sabadini, Irene; Shapiro, Michael; Struppa, Daniele C. A new characterization of a class of pseudoconvex domains in $ {\mathbb{C}}^{2}$. Comptes Rendus. Mathématique, Tome 344 (2007) no. 11, pp. 677-680. doi: 10.1016/j.crma.2007.04.014

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

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

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

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

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