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In the late ten years, the resolution of the equation $\bar\partial u=f$ withsharp estimates has been intensively studied for convex domains of finite typeby many authors. In this paper, we consider the case of lineally convexdomains. As the method used to obtain global estimates for a support functioncannot be carried out in this case, we use a kernel that does not givesdirectly a solution of the $\bar\partial$-equation but only a representationformula 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 setsof the functions of the Nevanlinna class for lineally convex domains of finitetype.

journal of geometric analysis/the journal of geometric analysis

Estimates for solutions of the $\partial$-equation and application to  the characterization of the zero varieties of the functions of the nevanlinna  class for lineally convex domains of finite type