On the singular numbers for some integral operators (Q5956914)

Let \(H\) be a separable Hilbert space. Given a compact operator \(T : H \to H,\) the singular numbers \(s_j(T)\) are defined as non-negative eigenvalues of the operator \((T^*T)^{1/2}\). A Schatten-von Neumann norm of \(T\) is defined by \[ ||t||= \Big ( \sum\limits_j s_j^p (T) \Big)^{1/p}, \quad 1 \leq p \leq \infty. \] Two-sided estimates of this norm are obtained for weighted Volterra integral operators and some potential-type operators on \(R^n\).