Theorems of Jackson type in $H^p$, $0<p<1$

In this paper an analogue of Jackson's inequality is established for the Hardy spaces $H^p$ $(0<p<1)$: if $f^{(k)}\in H^p$, then
$$ E_n(f)_p=O\biggl((n+1)^{-k}\omega_l\biggl(\frac1{n+1},\frac{\partial^kf}{\partial\varphi^k}\biggr)_{\!p}\,\biggr),\quad\text{as}\quad n\to\infty, $$
$k=0,1,\dots$; $ l=1,2,\dots$, and $\partial^kf/\partial\varphi^k=\lim_{r\to1-0}{\partial^kf(re^{i\varphi})}/{\partial\varphi^k}$.
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