科研之友
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摘要
Essentially sharp Markov-type inequalities are known for various classes of polynomials with constraints including constraints of the coefficients of the polynomials. For N and delta > 0 we introduce the class F(n,delta) as the collection of all polynomials of the form P(x) = Sigma(n)(k=h) a(k)x(k), a(k) is an element of Z, vertical bar a(k)vertical bar <= n(delta), vertical bar a(h)vertical bar = max(h <= k <= n)vertical bar a(k)vertical bar. In this paper, we prove essentially sharp Markov-type inequalities for polynomials from the classes F(n,delta) on [0, 1]. Our main result shows that the Markov factor 2n(2) valid for all polynomials of degree at most n on [0, 1] improves to c(delta)n log(n 1) for polynomials in the classes F(n,delta) d on [0, 1].
