Asymptotic Behavior of the Singular Values of Fractional Integral Operators

In this paper we find the precise asympotic of the singular numbers of the fractional integral operator Iα=∫x0(x − y)α − 1Γ(α)•dy in the case 0 < α ≤ 1/2 and improve the known estimates for 1/2 < α < 1. Also, we obtain some results concerning the precise asympotic of the singular numbers of convolution operators similar to the fractional integral operators.