The compactness of a weakly singular integral operator on weighted Sobolev spaces

It is shown that the weakly singular integral operator ∫ 1-1(Φ(τ)/|τ - t|^γ) dτ, where 0 < γ < 1, maps the weighted Sobolev space W (n)p;α,β (Ω) compactly into itself from 1 < p < ∞, 0 < α + 1/q, β + 1/q < 1 and n ∈ ℕ₀.