Approximation of a Wiener process by integrals with respect to the fractional Brownian motion of power functions of a given exponent

The best uniform approximation of a Wiener process by integrals of the form \[ \int _{0}^{t}f(s) dB_{s}^{H}\] is established in the space $L_{\infty } ([0,T];L_{2} (\Omega ))$, where $\{ B_{t}^{H}, t\in [0, T]\}$ is the fractional Brownian motion with the Hurst index $H$ and $f(s)=k\cdot s^{\alpha }$, $s\in [0,T]$, for $k>0$ and $\alpha =H-1/2$.