Approximation And Entropy Numbers Of Volterra Operators With Application To Brownian Motion

We consider the Volterra integral operator $T_{\rho,\psi}:L_p(0,\infty)\to L_q(0,\infty)$ for $1<p,q<\infty$, defined by $(T_{\rho,\psi}f)(s) =\rho(s)\int_0^s \psi(t) f(t) dt$ and investigate its degree of compactness in terms of properties of the kernel functions $\rho$ and $\psi$.