An Andreotti-Grauert Theorem with $l^r$ Estimates

Details An Andreotti-Grauert Theorem with $l^r$ Estimates An Andreotti-Grauert Theorem with $l^r$ Estimates

2012-03-04

arxiv.org/abs/1203.0759v2

Mathematics

Complex Variables

More precise important details thanks to C. Laurent

Scientific paper

By a theorem of Andreotti and Grauert if $\omega $ is a $(p,q)$ -current, $q < n,$ in a Stein manifold, $\bar{\partial}$ closed and with compact support, then there is a solution $u$ to $\bar{\partial}u=\omega $ still with compact support. The aim of this work is to show that if moreover $\omega \in L^{r}(dm),$ where $m$ is a suitable Lebesgue measure on the Stein manifold, then we have a solution $u$ with compact support {\sl and} in $L^{r}(dm).

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