Weighted $C^k$ estimates for a class of integral operators on non-smooth domains

Details Weighted $C^k$ estimates for a class of integral operators on non-smooth domains Weighted $C^k$ estimates for a class of integral operators on non-smooth domains

2009-03-24

arxiv.org/abs/0903.4082v1

Mathematics

Complex Variables

32 pages

Scientific paper

We apply integral representations for $(0,q)$-forms, $q\ge1$, on non-smooth
strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted
$C^k$ estimates for a given $(0,q)$-form, $f$, in terms of $C^k$ norms of
$\mdbar f$, and $\mdbar^{\ast} f$. The weights are powers of the gradient of
the defining function of the domain.

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