Geodesic
On the approximation by algebraic polynomials of functions of class~$L^p$, $0$
Izvestiya. Mathematics , Tome 11 (1977) no. 3, pp. 613-623

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In the article, Whitney's inequality $$ E_{k-1}(f;[a,b])\leqslant M_k\omega_k\biggl(\frac{b-a}k,f\biggr) $$ for bounded functions $f$ on $[a,b]$ is extended to the case $f\in L^p(a,b)$ for $0$. Bibliography: 10 titles. 
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     author = {\`E. A. Storozhenko},
     title = {On the approximation by algebraic polynomials of functions of class~$L^p$, $0<p<1$},
     journal = {Izvestiya. Mathematics },
     pages = {613--623},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a7/}
}
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È. A. Storozhenko. On the approximation by algebraic polynomials of functions of class~$L^p$, $0