AN ANDREOTTI-GRAUERT THEOREM WITH $L^r$ ESTIMATES.
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T02:59:44Z | |
| dc.date.available | 2024-04-04T02:59:44Z | |
| dc.date.created | 2019-10-09 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192763 | |
| dc.description.abstractEn | By a theorem of Andreotti and Grauert if $\omega $ is a $(p,q)$ current, $q < n,$ in a Stein manifold $\displaystyle \Omega ,\ \bar \partial $ closed and with compact support, then there is a solution $u$ to $\bar \partial u=\omega $ still with compact support in $\displaystyle \Omega .$ The main result of this work is to show that if moreover $\displaystyle \omega \in L^{r}(m),$ where $m$ is a suitable Lebesgue measure on the Stein manifold, then we have a solution $u$ with compact support {\sl and} in $L^{s}(m),\ \frac{1}{s}=\frac{1}{r}-\frac{1}{2(n+1)}.$ We prove it by estimates in $L^{r}$ spaces with weights. | |
| dc.language.iso | en | |
| dc.subject | d_bar | |
| dc.subject | compact support | |
| dc.title.en | AN ANDREOTTI-GRAUERT THEOREM WITH $L^r$ ESTIMATES. | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1203.0759 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00676110 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00676110v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AMAR,%20Eric&rft.genre=preprint |
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