论文信息 - Multivariate Bernstein and Markov inequalities

Multivariate Bernstein and Markov inequalities

Abstract For a polynomial P n of total degree n and a bounded convex set S it will be shown that for 0 p ⩽ ∞ ‖ ∂ ∂ξ P n ‖ L p (s) ⩽ Cn 2 ∦P n ∦L p(s) with C independent of n and of P n ϵ Π n . The Bernstein inequality ‖√1−x 2 d dx P n (x)‖L p [−1,1] ⩽ Cn ∦P n ∦L p[−1,1] will also be generalized and that generalization will be the crucial result. Theorems for higher and mixed derivatives will be achieved.

Z. Ditzian

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