Abstract

Let Ω be a smoothly bounded convex domain of finite type in Cⁿ. We show that a divisor in Ω satisfying the Blaschke condition (respectively associated to a current of order a > 0) can be defined by a function in the Nevanlinna class N₀(Ω) (respectively the Nevanlinna-Djrbachian class N_a(Ω)). The proof is based on L¹(bΩ) estimates (resp. weighted L¹(Ω) estimates) for the solution of the ∂-equation on Ω.

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