Search: MSC category 32W05 ( $\overline\partial$ and $\overline\partial$-Neumann operators )
 Growth Spaces and Growth Norm Estimates for $\Bar\partial$ on Convex Domains of Finite Type We consider the growth norm of a measurable function $f$ defined by $$\|f\|_{-\sigma}=\ess\{\delta_D(z)^\sigma|f(z)|:z\in D\},$$ where $\delta_D(z)$ denote the distance from $z$ to $\partial D$. We prove some optimal growth norm estimates for $\bar\partial$ on convex domains of finite type. Categories:32W05, 32A26, 32A36