On estimates for weighted Bergman projections
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CHARPENTIER, Philippe | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DUPAIN, Yves | |
| hal.structure.identifier | Chercheur indépendant | |
| dc.contributor.author | MOUNKAILA, , Modi | |
| dc.date.accessioned | 2024-04-04T02:18:31Z | |
| dc.date.available | 2024-04-04T02:18:31Z | |
| dc.date.issued | 2015-12 | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189322 | |
| dc.description.abstractEn | In this note we show that the weighted $L^{2}$-Sobolev estimates obtained by P. Charpentier, Y. Dupain \& M. Mounkaila for the weighted Bergman projection of the Hilbert space $L^{2}\left(\Omega,d\mu_{0}\right)$ where $\Omega$ is a smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^{n}$ and $\mu_{0}=\left(-\rho_{0}\right)^{r}d\lambda$, $\lambda$ being the Lebesgue measure, $r\in\mathbb{Q}_{+}$ and $\rho_{0}$ a special defining function of $\Omega$, are still valid for the Bergman projection of $L^{2}\left(\Omega,d\mu\right)$ where $\mu=\left(-\rho\right)^{r}d\lambda$, $\rho$ being any defining function of $\Omega$. In fact a stronger directional Sobolev estimate is established. Moreover similar generalizations are obtained for weighted $L^{p}$-Sobolev and lipschitz estimates in the case of pseudoconvex domain of finite type in $\mathbb{C}^{2}$ and for some convex domains of finite type. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.subject.en | pseudo-convex | |
| dc.subject.en | finite type | |
| dc.subject.en | Levi form locally diagonalizable | |
| dc.subject.en | convex | |
| dc.subject.en | weighted Bergman projection | |
| dc.subject.en | $\overline{\partial}_{\varphi}$-Neumann problem} | |
| dc.title.en | On estimates for weighted Bergman projections | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1090/proc/12660 | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1403.3412 | |
| bordeaux.journal | Proceedings of the American Mathematical Society | |
| bordeaux.page | 5337-5352 | |
| bordeaux.volume | 143 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 12 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00958898 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00958898v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.date=2015-12&rft.volume=143&rft.issue=12&rft.spage=5337-5352&rft.epage=5337-5352&rft.eissn=0002-9939&rft.issn=0002-9939&rft.au=CHARPENTIER,%20Philippe&DUPAIN,%20Yves&MOUNKAILA,%20,%20Modi&rft.genre=article |
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