= Shrinking-cutoff exponential-type estimate
{title2=$|\widehat u(z)|\leq C(1+|z|)^M e^{H_K(\operatorname{Im}z)}$}
Let a <distribution> have support in a <compact convex set> $K$. Fixed neighborhood cutoffs initially give an exponential bound larger than the <support function> $H_K$. Cutoffs of width $\varepsilon$ cost powers of $\varepsilon^{-1}$ in derivative estimates but enlarge the exponential by only $e^{C\varepsilon|\operatorname{Im}z|}$. Choosing $\varepsilon=(1+|z|)^{-1}$ absorbs the cutoff cost into a polynomial and retains the exact exponential $e^{H_K(\operatorname{Im}z)}$.
Back to article page
