Springer Online Journal Archives 1860-2000
Abstract For the weights exp (−|x|λ), 0〈λ≤1, we prove the exact analogue of the Markov-Bernstein inequality. The Markov-Bernstein constant turns out to be of order logn for λ=1 and of order 1 for 0〈λ〈1. The proof is based on the solution of the problem of how fast a polynomialP n can decrease on [−1,1] ifP n (0)=1. The answer to this problem has several other consequences in different directions; among others, it leads to a general theorem about the incompleteness of the set of polynomials in weightedL p spaces.
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