Henkin-Ramirez formulas with weight factors

Abstract

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 of domains in C n .

Locations

• French digital mathematics library (Numdam) - View - PDF
• Annales de l’institut Fourier - View - PDF