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Henkin-Ramirez formulas with weight factors

B. Berndtsson, Mats Andersson (1982)

Annales de l'institut Fourier

We construct a generalization of the Henkin-Ramírez (or Cauchy-Leray) kernels for the ∂ ‾ -equation. The generalization consists in multiplication by a weight factor and addition of suitable lower order terms, and is found via a representation as an “oscillating integral”. As special cases we consider weights which behave like a power of the distance to the boundary, like exp- ϕ with ϕ convex, and weights of polynomial decrease in C n . We also briefly consider kernels with singularities on subvarieties...

Hilbert-valued forms and barriers on weakly pseudoconvex domains.

Vincent Thilliez (1998)

Publicacions Matemàtiques

We introduce an alternative proof of the existence of certain Ck barrier maps, with polynomial explosion of the derivatives, on weakly pseudoconvex domains in Cn. Barriers of this sort have been constructed very recently by J. Michel and M.-C. Shaw, and have various applications. In our paper, the adaptation of Hörmander's L2 techniques to suitable vector-valued functions allows us to give a very simple approach of the problem and to improve some aspects of the result of Michel and Shaw, regarding...

Hölder and Lp estimates for the solutions of the ∂-equation in non-smooth strictly pseudoconvex domains.

Josep M. Burgués Badía (1990)

Publicacions Matemàtiques

Let D be a bounded strict pseudoconvex non-smooth domain in Cn. In this paper we prove that the estimates in Lp and Lipschitz classes for the solutions of the ∂-equation with Lp-data in regular strictly pseudoconvex domains (see [2]) are also valid for D. We also give estimates of the same type for the ∂b in the regular part of the boundary of these domains.

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