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

The domain Λ k , T s f of the Wiener integral with respect to a sub-fractional Brownian motion ( S t k ) t ∈ [ 0 , T ] , k ∈ ( − 1 2 , 1 2 ) , k ≠ 0 , is characterized. The set Λ k , T s f is a Hilbert space which contains the class of elementary functions as a dense subset. If k ∈ ( − 1 2 , 0 ) , any element of Λ k , T s f is a function and if k ∈ ( 0 , 1 2 ) , the domain Λ k , T s f is a space of distributions.