  Let $B_H(\cdot)$ be a fractional Brownian motion with Hurst parameter
$H\in(0,1]$. Motivated by applications to maximal inequalities for fractional
Brownian motion, in this note we derive bounds for
K_T(H,\gamma):=E[\sup_{t\in[0,T]}|B_H(t)|]^\gamma, with $\gamma, T>0$.
