Geodesic
Application of a~Bernstein-type inequality to rational interpolation in the Dirichlet space
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 101-112

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We prove a Bernstein-type inequality involving the Bergman and Hardy norms, for rational functions in the unit disk $\mathbb D$ having at most $n$ poles all outside of $\frac1r\mathbb D$, $0$. The asymptotic sharpness of this inequality is shown as $n\to\infty$ and $r\to1^-$. We apply our Bernstein-type inequality to an efficient Nevanlinna–Pick interpolation problem in the standard Dirichlet space, constrained by the $H^2$-norm. 
@article{ZNSL_2011_389_a5,
     author = {R. Zarouf},
     title = {Application of {a~Bernstein-type} inequality to rational interpolation in the {Dirichlet} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {101--112},
     publisher = {mathdoc},
     volume = {389},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a5/}
}
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R. Zarouf. Application of a~Bernstein-type inequality to rational interpolation in the Dirichlet space. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 101-112. http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a5/