Estimates $ L^{r}-L^{s}$ for solutions of the $\bar \partial $ equation in strictly pseudo convex domains in ${\mathbb{C}}^{n}.$
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T02:20:07Z | |
| dc.date.available | 2024-04-04T02:20:07Z | |
| dc.date.created | 2013-12 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189466 | |
| dc.description.abstractEn | We prove estimates for solutions of the $\bar \partial u=\omega $ equation in a strictly pseudo convex domain $ \Omega $ in ${\mathbb{C}}^{n}.$ For instance if the $ (p,q)$ current $\omega $ has its coefficients in $L^{r}(\Omega )$ with $1\leq r<2(n+1)$ then there is a solution $u$ in $L^{s}(\Omega )$ with $\ \frac{1}{s}=\frac{1}{r}-\frac{1}{2(n+1)}.$ We also have $BMO$ and Lipschitz estimates for $r\geq 2(n+1).$ These results were already done by S. Krantz in the case of $(0,1)$ forms and just for the $L^{r}-L^{s}$ part by L. Ma and S. Vassiliadou for general $(p,q)$ forms. To get the complete result we propose another approach, based on Carleson measures of order $\alpha $ and on the subordination lemma. | |
| dc.language.iso | en | |
| dc.subject | Carleson measures | |
| dc.subject | d_bar equation | |
| dc.title.en | Estimates $ L^{r}-L^{s}$ for solutions of the $\bar \partial $ equation in strictly pseudo convex domains in ${\mathbb{C}}^{n}.$ | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1312.7136 | |
| 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-00922356 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00922356v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AMAR,%20Eric&rft.genre=preprint |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||