Skalyga, V. I. 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. Reviewer: Dan Bārbosu (Baia Mare) 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) Keywords:Bernstein inequality; Markov inequality; convex bodies PDF BibTeX XML Cite \textit{V. I. Skalyga}, Izv. Math. 65, No. 6, 1197--1241 (2001; Zbl 1026.41011); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 65, No. 6, 129--172 (2001) Full Text: DOI