Real boundary bounds for a unit-disc H-hull
= Real boundary bounds for a unit-disc H-hull
{title2=$x\leq g_K(x)\leq x+x^{-1}\quad(x>1)$}
If a <compact H-hull> lies in the unit disc, compare its tail <harmonic measure> with that of the empty hull and filled half-disc. The <Poisson kernel for the upper half-plane> turns the inclusion of Brownian exit events into $x\leq g_K(x)\leq x+1/x$ for $x>1$. Reflection gives $x+1/x\leq g_K(x)\leq x$ for $x<-1$.