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 $10$. We also obtain similar sharp estimates for the approximation numbers of $T_{\rho,\psi}$, thus extending former results due to Edmunds et al. and Evans et al..The entropy estimates are applied to investigate the small ball behaviour of weighted Wiener processes $\rho W$ in the $L_q(0,\infty)$-norm, $1