On estimates of the approximation numbers of the Hardy operator

E. N. Lomakina

Eurasian mathematical journal, Tome 6 (2015) no. 2, pp. 41-62

Résumé

We obtain two–sided estimates which describe the behaviour of the approximation numbers of the Hardy operator and Schatten–Neumann norms in the new case, when the compact operator $$ Tf(x)=\int_0^x f(\tau) d\tau, \quad x>0, $$ is acting from a Lebesgue space to a Lorentz space $(T: L_v^r(R^+)\to L_\omega^{pq}(R^+))$ under the condition $1$.