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.

MSC Classifications:

32W05, 32A26, 32A36 show english descriptions $\overline\partial$ and $\overline\partial$-Neumann operators
Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)
Bergman spaces 32W05 - $\overline\partial$ and $\overline\partial$-Neumann operators
32A26 - Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)
32A36 - Bergman spaces

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