Arestov's theorems on Bernstein's inequality

2019/04/26 by Erdélyi, Tamás · 1 citation
#41A17 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.11887

Abstract

We give a simple, elementary, and at least partially new proof of Arestov's famous extension of Bernstein's inequality in L_p to all p ≥ 0. Our crucial observation is that Boyd's approach to prove Mahler's inequality for algebraic polynomials P_n ∈ \mathcal P_n^c can be extended to all trigonometric polynomials T_n ∈ \mathcal T_n^c.

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