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Multidimensional analogues of the Markov and Bernstein inequalities. (English. Russian original) Zbl 1026.41011
Izv. Math. 65, No. 6, 1197-1241 (2001); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 65, No. 6, 129-172 (2001).
The author establishes analogous of Bernstein’s and Markov’s inequalities for the case of multivariate functions. He obtains estimates for the derivatives of algebraic polynomials on convex bodies and centrally symmetric convex bodies.
MSC:
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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