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L1 and L∞-estimates with a local weight for the ∂-equation on convex domains in Cn.

Francesc Tugores (1992)

Publicacions Matemàtiques

We construct a defining function for a convex domain in Cn that we use to prove that the solution-operator of Henkin-Romanov for the ∂-equation is bounded in L1 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 the...

Levi-equation in higher dimensions

Zbginiew Slodkowski, Giuseppe Tomassini (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We announce some results concerning the Dirichlet problem for the Levi-equation in C n . We consider for the sake of simplicity the case n = 3 .

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