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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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