Geodesic
Weighted Markov-Bernstein Inequalities for Entire Functions of Exponential Type
Publications de l'Institut Mathématique, _N_S_96 (2014) no. 110, p. 181 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
@article{PIM_2014_N_S_96_110_a13,
     author = {Doron S. Lubinsky},
     title = {Weighted {Markov-Bernstein} {Inequalities} for {Entire} {Functions} of {Exponential} {Type}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {181 },
     year = {2014},
     volume = {_N_S_96},
     number = {110},
     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/