hal-00676110, version 2
AN ANDREOTTI-GRAUERT THEOREM WITH $L^r$ ESTIMATES.
(03/03/2012)
Résumé : By a theorem of Andreotti and Grauert if $\omega $ is a $(p,q)$ -current, $q < n,$ in a Stein manifold, $\bar{\partial }$ closed and with compact support, then there is a solution $u$ to $\bar{\partial }u=\omega $ still with compact support. The aim of this work is to show that if moreover $\omega \in L^{r}(dm),$ where $m$ is a suitable Lebesgue measure on the Stein manifold, then we have a solution $u$ with compact support {\sl and} in $L^{r}(dm).
- 1 :
- CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
- Domaine : Mathématiques/Variables complexes
- Mots-clés : d_bar – compact support
- Commentaire : More precise important details thanks to C. Laurent.
- Versions disponibles : v1 (04-03-2012) v2 (05-04-2012) v3 (26-10-2012) v4 (23-11-2012) v5 (13-12-2012)
- hal-00676110, version 2
- http://hal.archives-ouvertes.fr/hal-00676110
- oai:hal.archives-ouvertes.fr:hal-00676110
- Contributeur :
- Soumis le : Jeudi 5 Avril 2012, 10:47:11
- Dernière modification le : Jeudi 5 Avril 2012, 15:13:18
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