Weighted and boundary l p estimates for solutions of the ∂ -equation on lineally convex domains of finite type and applications
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CHARPENTIER, Ph. | |
| hal.structure.identifier | Auteur indépendant | |
| dc.contributor.author | DUPAIN, Y | |
| dc.date.accessioned | 2024-04-04T03:10:19Z | |
| dc.date.available | 2024-04-04T03:10:19Z | |
| dc.date.created | 2017-04-12 | |
| dc.date.issued | 2018-10 | |
| dc.identifier.issn | 0025-5874 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193680 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | Springer | |
| dc.subject.en | lineally convex | |
| dc.subject.en | finite type | |
| dc.subject.en | Bergman projection | |
| dc.title.en | Weighted and boundary l p estimates for solutions of the ∂ -equation on lineally convex domains of finite type and applications | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00209-017-2015-8 | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1704.03762 | |
| bordeaux.journal | Mathematische Zeitschrift | |
| bordeaux.page | 195-220 | |
| bordeaux.volume | 290 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1-2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01507115 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01507115v1 | |
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