Cohomology of sheaves of holomorphic functions satisfying boundary conditions on product domains

Nagel, Alexander

doi:10.1090/S0002-9947-1972-0320363-2

Cohomology of sheaves of holomorphic functions satisfying boundary conditions on product domains
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Trans. Amer. Math. Soc. 172 (1972), 133-141 Request permission

Abstract:

This paper considers sheaves of germs of holomorphic functions which satisfy certain boundary conditions on product domains in ${{\mathbf {C}}^n}$. Very general axioms for boundary behavior are given. This includes as special cases ${L^p}$ boundary behavior, $1 \leq p \leq \infty$; continuous boundary behavior; differentiable boundary behavior of order $m,0 \leq m \leq \infty$, with an additional Hölder condition of order $\alpha ,0 \leq \alpha \leq 1$, on the $m$th derivatives. A fine resolution is constructed for those sheaves considered, and the main result of the paper is that all higher cohomology groups for these sheaves are zeŕo.

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