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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.

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