The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions

These results can be applied, for instance, to Abel kernels and to the Volterra function I(x)=μ(x,0,−1)=∫0∞xs−1/Γ(s)ds, the latter being relevant for instance in the analysis of the Schrödinger equation with concentrated nonlinearities in R2.