Arestov’s theorems on Bernstein’s inequality Academic Article uri icon


  • 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 $p geq 0$. Our crucial observation is that Boyd's approach to prove Mahler's inequality for algebraic polynomials $P_n in {mathcal P}_n^c$ can be extended to all trigonometric polynomials $T_n in {mathcal T}_n^c$.

published proceedings

  • Journal of Approximation Theory

author list (cited authors)

  • Erdélyi, T.

citation count

  • 4

complete list of authors

  • Erdélyi, Tamás

publication date

  • February 2020