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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- with convex, and weights of polynomial decrease in . We also briefly consider kernels with singularities on subvarieties...
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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