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Weighted and boundary l p estimates for solutions of the ∂ -equation on lineally convex domains of finite type and applications

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCHARPENTIER, Ph.
hal.structure.identifierAuteur indépendant
dc.contributor.authorDUPAIN, Y
dc.date.accessioned2024-04-04T03:10:19Z
dc.date.available2024-04-04T03:10:19Z
dc.date.created2017-04-12
dc.date.issued2018-10
dc.identifier.issn0025-5874
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193680
dc.description.abstractEnWe obtain sharp weighted estimates for solutions of the equation ∂ u = f in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces L p (Ω,δ γ), δ being the distance to the boundary, with two different types of hypothesis on the form f : first, if the data f belongs to L p Ω,δ γ Ω , γ > −1, we have a mixed gain on the index p and the exponent γ; secondly we obtain a similar estimate when the data f satisfies an apropriate anisotropic L p estimate with weight δ γ+1 Ω. Moreover we extend those results to γ = −1 and obtain L p (∂ Ω) and BMO(∂ Ω) estimates. These results allow us to extend the L p (Ω,δ γ)-regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights.
dc.language.isoen
dc.publisherSpringer
dc.subject.enlineally convex
dc.subject.enfinite type
dc.subject.enBergman projection
dc.title.enWeighted and boundary l p estimates for solutions of the ∂ -equation on lineally convex domains of finite type and applications
dc.typeArticle de revue
dc.identifier.doi10.1007/s00209-017-2015-8
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.identifier.arxiv1704.03762
bordeaux.journalMathematische Zeitschrift
bordeaux.page195-220
bordeaux.volume290
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1-2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01507115
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01507115v1
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