Two problems associated with convex finite type domains.

Alexander Iosevich; Eric Sawyer; Andreas Seeger

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Solution of the $\bar{\partial}$ -equation on non-smooth strictly $q$ -concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem

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Laura De Carli, Enrico Laeng (2000)

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L and L-estimates with a local weight for the ∂-equation on convex domains in C.

Francesc Tugores (1992)

Publicacions Matemàtiques

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We construct a defining function for a convex domain in C that we use to prove that the solution-operator of Henkin-Romanov for the ∂-equation is bounded in L and L-norms with a weight that reflects not only how near the point is to the boundary of the domain but also how convex the domain is near the point. We refine and localize the weights that Polking uses in [Po] for the same type of domains because they depend only on the Euclidean distance to the boudary and don't take into account...