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 - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Geometric Analysis Année : 2014

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

Yves Dupain
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Modi Mounkaila,
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Résumé

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.
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Dates et versions

hal-00563932 , version 1 (07-02-2011)
hal-00563932 , version 2 (19-02-2013)

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Citer

Philippe Charpentier, Yves Dupain, Modi Mounkaila,. 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. Journal of Geometric Analysis, 2014, 24 (4), pp.1860-1881. ⟨10.1007/s12220-013-9398-5⟩. ⟨hal-00563932v2⟩

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