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Mat. Zametki, 1968, Volume 3, Issue 4, Pages 431–440 (Mi mz6699)  

Some inequalities of the V. A. Markov type

V. A. Andreeva, V. M. Chevskii


Abstract: Let $B$ be a domain in the complex plane, let $p_n(z)$ and $P_n(z)$ be polynomials of degree $n$ where the zeros of $P_n(z)$ lie in $\overline B$, let $\varphi(z)$ be a finite function, $\varphi(z)\ne0$, $z\overline\in\overline B$. We consider the problem of estimating from above the functions $L[p_n(z)]=\varphi p_n'(z)-wp_n(z), \overline\in\overline B$, если $|p_n(z)|\leqslant+|P_n(z)|$ при $z\in\overline B$. Under some very general conditions on $B$, $z$, $\varphi(z)$ and $w$ we prove the inequality $|L[p_n(z)]|\leqslant|L[P_n(z)]|$.

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English version:
Mathematical Notes, 1968, 3:4, 275–280

Bibliographic databases:

UDC: 517.5
Received: 29.06.1967

Citation: V. A. Andreeva, V. M. Chevskii, “Some inequalities of the V. A. Markov type”, Mat. Zametki, 3:4 (1968), 431–440; Math. Notes, 3:4 (1968), 275–280

Citation in format AMSBIB
\Bibitem{AndChe68}
\by V.~A.~Andreeva, V.~M.~Chevskii
\paper Some inequalities of the V.\,A.~Markov type
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 4
\pages 431--440
\mathnet{http://mi.mathnet.ru/mz6699}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=226032}
\zmath{https://zbmath.org/?q=an:0177.09803|0174.11302}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 4
\pages 275--280
\crossref{https://doi.org/10.1007/BF01159945}


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