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

Raffaele Carlone, Alberto Fiorenza, Lorenzo Tentarelli

For kernels $\nu$ which are positive and integrable we show that the operator $g\mapsto J_{\nu }g={\int }_0^x\nu (x-s)g(s)ds$ on a finite time interval enjoys a regularizing effect when applie…