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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCHARPENTIER, Philippe
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDUPAIN, Yves
hal.structure.identifierChercheur indépendant
dc.contributor.authorMOUNKAILA, , Modi
dc.date.accessioned2024-04-04T02:18:31Z
dc.date.available2024-04-04T02:18:31Z
dc.date.issued2015-12
dc.identifier.issn0002-9939
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189322
dc.description.abstractEnIn 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.isoen
dc.publisherAmerican Mathematical Society
dc.subject.enpseudo-convex
dc.subject.enfinite type
dc.subject.enLevi form locally diagonalizable
dc.subject.enconvex
dc.subject.enweighted Bergman projection
dc.subject.en$\overline{\partial}_{\varphi}$-Neumann problem}
dc.title.enOn estimates for weighted Bergman projections
dc.typeArticle de revue
dc.identifier.doi10.1090/proc/12660
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.identifier.arxiv1403.3412
bordeaux.journalProceedings of the American Mathematical Society
bordeaux.page5337-5352
bordeaux.volume143
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue12
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00958898
hal.version1
hal.popularnon
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00958898v1
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