Zero sets of functions in the Nevanlinna or the Nevanlinna–Djrbachian classes

Anne Cumenge

Vol. 199 (2001), No. 1, 79–92

DOI: 10.2140/pjm.2001.199.79

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.

Milestones

Received: 18 August 1999

Published: 1 May 2001