On S. M. Nikol'skii type inequalities between different metrics

The paper is devoted to the derivation of analogs of S. M. Nikol'skii type inequalities for algebraic polynomials in weighted spaces and for rather general classes of curves in the complex plane. We announced similar inequalities for less general classes of curves and simpler weight functions earlier and in joint papers with I. I. Ibragimov. The order optimality of the inequalities follows from the obtained corollaries, which hold for a closed interval of the real line.
Note that similar inequalities on the real line were obtained by S. M. Nikol'skii, N. K. Bari, I. I. Ibragimov, S. B. Stechkin, A. F. Timan, V. V. Arestov, and others.