Estimates for Solutions of the $\partial$-Equation and Application to the Characterization of the Zero Varieties of the Functions of the Nevanlinna Class for Linearly Convex Domains of Finite Type
Language
en
Article de revue
This item was published in
Journal of Geometric Analysis. 2014, vol. 24, n° 4, p. 1860-1881
English Abstract
In the late ten years, the resolution of the equation $\bar\partial u=f$ with sharp estimates has been intensively studied for convex domains of finite type by many authors. In this paper, we consider the case of lineally ...Read more >
In the late ten years, the resolution of the equation $\bar\partial u=f$ with sharp estimates has been intensively studied for convex domains of finite type by many authors. In this paper, we consider the case of lineally convex domains. As the method used to obtain global estimates for a support function cannot be carried out in this case, we use a kernel that does not gives directly a solution of the $\bar\partial$-equation but only a representation formula which allows us to end the resolution of the equation using Kohn's $L^2$ theory. As an application we give the characterization of the zero sets of the functions of the Nevanlinna class for lineally convex domains of finite type.Read less <
English Keywords
lineally convex
finite type
$\bar\partial$-equation
Nevanlinna class
Origin
Hal imported