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

Abstract

Let Ω be a smoothly bounded convex domain of finite type in C n . 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 N 0 (Ω) (respectively the Nevanlinna-Djrbachian class N a (Ω)). The proof is based on L 1 (bΩ) estimates (resp. weighted L 1 (Ω) estimates) for the solution of the∂-equation on Ω.

Weighted $L^p$ estimates for the $\bar\partial$-equation on convex domains of finite type

“…Diederich-Mazzilli [DM01] (resp. Cumenge [Cum01b]) obtained the characterization of the zero sets of functions in the Nevanlinna (resp. Nevanlinna-Djrbachian) classes using non-isotropic L 1 (bΩ) (resp.…”

OPTIMAL NON-ISOTROPIC Lp ESTIMATES WITH WEIGHTS FOR ∂ IN STRICTLY PSEUDOCONVEX DOMAINS

“…For the weakly pseudoconvex domains, Bruna et al [2] recently showed non-isotropic L 1 estimates and Cumenge [3] proved non-isotropic L 1 estimates with weights in convex domains of finite type.…”

Entire Functions of Bounded L-Index: Its Zeros and Behavior of Partial Logarithmic Derivatives

“…To deduce (18), we implicitly used that Condition (11) provides (19). Indeed, we will find a lower estimate of measure of the set T (…”

“…The different estimates of measure of zero set and its geometrical properties are investigated in [17][18][19][20][21][22]. We suppose that zero points of entire functions admit uniform distribution in some sense, that is, (29).…”