Geodesic
Weighted Markov-Bernstein Inequalities for Entire Functions of Exponential Type
Publications de l'Institut Mathématique, _N_S_96 (2014) no. 110, p. 181

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We prove weighted Markov-Bernstein inequalities of the form $ ıt_{-ıty}^{ıfty}|f'(x)|^pw(x)\,dx eq C(igma+1)^pıt_{-ıty}^{ıfty}|f(x)|^pw(x)\,dx $ Here $w$ satisfies certain doubling type properties, $f$ is an entire function of exponential type $\leq\sigma$, $p>0$, and $C$ is independent of $f$ and $\sigma$. For example, $w(x)=(1+x^2)^{\alpha}$ satisfies the conditions for any $\alpha\in\mathbb{R}$. Classical doubling inequalities of Mastroianni and Totik inspired this result.
Classification : 42C05
Keywords: entire functions of exponential type, Bernstein inequalities 
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     author = {Doron S. Lubinsky},
     title = {Weighted {Markov-Bernstein} {Inequalities} for {Entire} {Functions} of {Exponential} {Type}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {181 },
     publisher = {mathdoc},
     volume = {_N_S_96},
     number = {110},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2014_N_S_96_110_a13/}
}
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Doron S. Lubinsky. Weighted Markov-Bernstein Inequalities for Entire Functions of Exponential Type. Publications de l'Institut Mathématique, _N_S_96 (2014) no. 110, p. 181 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_96_110_a13/