A Non-Linear Integral System

Abstract

Here we study the asymptotic behaviour of the eigenvalues of a non-linear integral system that arises from the problem of determining $\mathop {\rm {sup}}\limits_ {b\varepsilon T(B)}\|{\rm g}\|_q,$ where B is the closed unit ball in L _p (a,b) and $T:L_P(a,b)\longrightarrow L_p(a,b)$ is the Hardy operator. This enables us to give the asymptotic behaviour of the approximation and Kolmogorov numbers of T when q ≤ p and that of the Bernstein numbers of T when p ≤ q.