On a problem of Hardy-Littlewood

This work gives an estimate for the quasinorm of the $k$th derivative of a function in the Hardy space $H^p$, $0<p\leqslant\infty$, using a modulus of continuity of order $k$, specially introduced for $H^p$. Also considered are applications of the results to the problem of imbedding of Hardy classes and the theory of approximation.
Bibliography: 26 titles.