On the Wiener integral with respect to the fractional Brownian motion on an interval

We characterize the domain of the Wiener integral with respect to the fractional Brownian motion of any Hurst parameter H∈(0,1) on an interval [0,T]. The domain is the set of restrictions to D((0,T)) of the distributions of W1/2−H,2(R) with support contained in [0,T]. In the case H⩽1/2 any element of the domain is given by a function, but in the case H>1/2 this space contains distributions that are not given by functions. The techniques used in the proofs involve distribution theory and Fourier analysis, and allow to study simultaneously both cases H<1/2 and H>1/2.