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Article Dans Une Revue Mathematische Zeitschrift Année : 2018

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

Ph. Charpentier
Y Dupain
  • Fonction : Auteur

Résumé

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.
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Dates et versions

hal-01507115 , version 1 (12-04-2017)

Identifiants

Citer

Ph. Charpentier, Y Dupain. Weighted and boundary l p estimates for solutions of the ∂ -equation on lineally convex domains of finite type and applications. Mathematische Zeitschrift, 2018, 290 (1-2), pp.195-220. ⟨10.1007/s00209-017-2015-8⟩. ⟨hal-01507115⟩

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