Berndtsson, Andersson: Henkin-Ramirez formulas with weight factors

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B. Berndtsson; Mats Andersson
Henkin-Ramirez formulas with weight factors
Annales de l'institut Fourier, 32 no. 3 (1982), p. 91-110, doi: 10.5802/aif.881
Article PDF | Reviews MR 84j:32003 | Zbl 0466.32001 | 9 citations in Cedram

Résumé - Abstract

We construct a generalization of the Henkin-Ramírez (or Cauchy-Leray) kernels for the $\overline{\partial }$-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-$\phi $ with $\phi $ convex, and weights of polynomial decrease in ${\bf C}^n$. We also briefly consider kernels with singularities on subvarieties of domains in ${\bf C}^n$.

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