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Théorie L p et dualité de Serre pour l’équation de Cauchy-Riemann
Christine Laurent-Thiébaut
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 2, p. 251-279

In this paper we propose a systematic study of the Cauchy-Riemann operator in the L p -setting in complex manifolds. We first consider L loc p -theory and then we develop an L p Andreotti-Grauert theory. In the second half of the paper we consider Serre duality and its applications to the solvability of the Cauchy-Riemann equation with exact support in L p -spaces.

Dans cet article nous proposons une étude systématique de la théorie L p pour l’opérateur de Cauchy-Riemann dans les variétés complexes. Dans une première partie nous étudions la théorie L p locale puis nous développons la théorie d’Andreotti-Grauert dans le cadre L p . La seconde moitié de l’article est consacrée à la dualité de Serre et à ses applications à la résolution avec support exact de l’équation de Cauchy-Riemann dans les espaces L p .

Received : 2013-08-13
Accepted : 2015-01-05
Published online : 2015-05-27
DOI : https://doi.org/10.5802/afst.1448
@article{AFST_2015_6_24_2_251_0,
     author = {Christine Laurent-Thi\'ebaut},
     title = {Th\'eorie $L^p$ et dualit\'e de Serre pour l'\'equation de Cauchy-Riemann},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 24},
     number = {2},
     year = {2015},
     pages = {251-279},
     doi = {10.5802/afst.1448},
     mrnumber = {3358613},
     language = {fr},
     url = {https://afst.centre-mersenne.org/item/AFST_2015_6_24_2_251_0}
}
Laurent-Thiébaut, Christine. Théorie $L^p$ et dualité de Serre pour l’équation de Cauchy-Riemann. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 2, pp. 251-279. doi : 10.5802/afst.1448. afst.centre-mersenne.org/item/AFST_2015_6_24_2_251_0/

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