Bernstein inequalities with nondoubling weights

Andriy Bondarenko, Sergey Tikhonov

We answer Totik's question on weighted Bernstein's inequalities showing that $$\Vert T_n^{\prime }{\Vert }_{L_p(\omega )}\le C(p,\omega )n\Vert T_n{\Vert }_{L_p(\omega )},0<p\le \infty ,$$ holds for all trigonom…