An andreotti-grauert theorem with $l^r$ estimates

By a theorem of Andreotti and Grauert if $\omega$ is a $(p,q)$ current, $q < n,$inaSteinmanifold$\displaystyle \Omega ,\ \bar \partial $ closed and with compact support, then there is a solution $u$ to $\bar{\mathrm{\partial }}u=\omega$ still with compact support in ${\displaystyle \mathrm{\Omega }\mathrm{.}}$ The main result of this work is to show that if moreover ${\displaystyle \omega \in L^r(m),}$ where $m$ is a suitable Lebesgue measure on the Stein manifold, then we have a solution $u$ with compact support {\sl and} in $L^{s}(m),
\frac{1}{s}=\frac{1}{r}-\frac{1}{2(n+1)}.$Weproveitbyestimatesin$L^{r}$ spaces with weights.