Geodesic
Rational approximation in $L^p$ and Faber transforms
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 70-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the technique of Faber transforms we show that Pekarskii's theorem on rational approximation of functions in $H^p$, $1, directly implies Petrushev's theorem on rational approximation in $L^p[-1,1]$, $1, and vice versa. The same technique permits us to obtain similar results for functions analytic in domains with Lipschitz Jordan boundaries. 
@article{ZNSL_1987_157_a5,
     author = {V. V. Peller},
     title = {Rational approximation in~$L^p$ and {Faber} transforms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {70--75},
     year = {1987},
     volume = {157},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a5/}
}
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V. V. Peller. Rational approximation in $L^p$ and Faber transforms. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 70-75. http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a5/