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Markov and Bernstein inequalities in [L.sup.P] for some weighted algebraic and trigonometric polynomials.
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Bernstein inequalities are given for polynomials of degree at most 2m (where m [less than or equal to] n), weighted by [(1 + [x.sup.2]).sup.-n], in [L.sup.p] norms on (-[infinity],[infinity]), and also in related spaces of weighted trigonometric polynomials. Also, Bernstein and Markov inequalities valid on [0,[infinity]) are derived for polynomials of degree m weighted by [(1 + t).sup.-n].
1. Introduction
Let [[??].sub.m,n] (with m [less than or equal to] n) denote the space of polynomials of degree 2m or less on (-[infinity],[infinity]), weighted by ...
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