The Bergman projection and weighted $C^k$ estimates for the canonical solution to \dbar on non-smooth domains

Details The Bergman projection and weighted $C^k$ estimates for the canonical solution to \dbar on non-smooth domains The Bergman projection and weighted $C^k$ estimates for the canonical solution to \dbar on non-smooth domains

2009-03-24

arxiv.org/abs/0903.4087v1

Mathematics

Complex Variables

19 pages

Scientific paper

We apply integral representations for functions on non-smooth strictly
pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted $C^k$
estimates for the component of a given function, $f$, which is orthogonal to
holomorphic functions in terms of $C^k$ norms of $\mdbar f$. The weights are
powers of the gradient of the defining function of the domain.

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