Geodesic
Some estimates of derivatives of rational functions in integral metrics
Matematičeskie zametki, Tome 13 (1973) no. 4, pp. 499-510.

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Estimates are established in the metric of $L_q$ $($0

/(p+1)$, $0\le\infty$) of derivatives of a~rational function in terms of the norm of the function itself in the metric of $L_p$. Local norms in $L_p$ are also estimated of Taylor remainders of a~rational function in terms of its norm in $L_p$. 
@article{MZM_1973_13_4_a2,
     author = {E. A. Sevast'yanov},
     title = {Some estimates of derivatives of rational functions in integral metrics},
     journal = {Matemati\v{c}eskie zametki},
     pages = {499--510},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_4_a2/}
}
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E. A. Sevast'yanov. Some estimates of derivatives of rational functions in integral metrics. Matematičeskie zametki, Tome 13 (1973) no. 4, pp. 499-510. http://geodesic.mathdoc.fr/item/MZM_1973_13_4_a2/