Geodesic
Theorems of Jackson type in~$H^p$,~$0$
Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 203-218

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In this paper an analogue of Jackson's inequality is established for the Hardy spaces $H^p$ $(0$: 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 $\partial^kf/\partial\varphi^k=\lim_{r\to1-0}{\partial^kf(re^{i\varphi})}/{\partial\varphi^k}$. Bibliography: 15 titles. 
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     author = {\`E. A. Storozhenko},
     title = {Theorems of {Jackson} type in~$H^p$,~$0<p<1$},
     journal = {Izvestiya. Mathematics },
     pages = {203--218},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a8/}
}
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È. A. Storozhenko. Theorems of Jackson type in~$H^p$,~$0