Abstract
Following Arestov’s Λ-method we give a simple, elementary, and at least partially new proof of Arestov’s famous extension of Bernstein’s inequality in Lp to all p≥0. Our crucial observation is that Boyd’s approach to prove Mahler’s inequality for algebraic polynomials Pn∈Pnc can be extended to all trigonometric polynomials Tn∈Fnc.
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