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Analogs of Markov’s inequality in normed spaces. (English. Russian original) Zbl 1076.46036
Math. Notes 75, No. 5, 739-743 (2004); translation from Mat. Zametki 75, No. 5, 793-796 (2004).
The Markov inequality states $| P^{(k)}_n(x)| \leq c_{n,k}\| P_n\| _{C([-1,1])}\quad \text{ for } -1\leq x \leq 1, 0\leq k \leq n$ for all polynomials $$P_n(x)$$ of degree at most $$n$$ in one real variable $$x$$. The best constants $$c_{n,k}$$ are explicitly known and they are attained for the Chebyshev polynomials $$T_n(x)=\cos(n\cdot \arccos x)$$ at $$x=\pm1$$. In the paper under review, some generalizations of these inequalities are given for real valued polynomials on Banach spaces. The interesting paper does not contain any proofs.

##### MSC:
 46G25 (Spaces of) multilinear mappings, polynomials 26D99 Inequalities in real analysis
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