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- W2081728195 abstract "Recently, weighted Markov and Bernstein inequalities have been established for large classes of Freud weights, that is, weights of the form W ( x ) ≔ e − Q ( x ) , where Q ( x ) is even and of smooth polynomial growth at infinity. In this paper, we consider Erdős weights, which have the form W ( x ) ≔ e − Q ( x ), where Q ( x ) is even and of faster than polynomial growth at infinity. For a large class of Erdős weights, we establish the Markov type inequality ‖P ′ ‖ R ⩽CD ′ (a n )‖PW‖ R , (1) for n ⩾ 1 and P any polynomial of degree at most n . Here the norm is the sup norm, and C is independent of n and P , while a n is the Mhaskar-Rahmanov-Saff number, that is, it is the positive root of the equation n = 2 n ∝ 0 1 a n tQ′(a n t)dt √1 − t 2 For example, we consider Q ( x ) ≔exp k (|| α ), where α > 0, and where exp k denotes the k th iterated exponential, and give a more explicit formulation of (1). We also establish Bernstein type inequalities that for part of the range (− ∞, ∞) improve on (1)." @default.
- W2081728195 created "2016-06-24" @default.
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- W2081728195 date "1990-02-01" @default.
- W2081728195 modified "2023-09-30" @default.
- W2081728195 title "L∞ Markov and Bernstein inequalities for Erdös weights" @default.
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- W2081728195 doi "https://doi.org/10.1016/0021-9045(90)90084-4" @default.
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