We give a simple, elementary, and at least partially new proof of Arestovs famous extension of Bernsteins inequality in $L_p$ to all $p geq 0$. Our crucial observation is that Boyds approach to prove Mahlers inequality for algebraic polynomials $P_n in {mathcal P}_n^c$ can be extended to all trigonometric polynomials $T_n in {mathcal T}_n^c$.
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