Weighted estimates for solutions of the ∂ -equation for lineally convex domains of finite type and applications to weighted bergman projections

2016/05/09 by Charpentier, Philippe, Dupain, Y, Mounkaila, M
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.02443

Abstract

In this paper we obtain sharp weighted estimates for solutions of the ∂-equation in a lineally convex domains of finite type. Precisely we obtain estimates in spaces of the form L p (Ω,δ γ), δ being the distance to the boundary, with gain on the index p and the exponent γ. These estimates allow us to extend the L p (Ω,δ γ) and lipschitz regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights.

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