Constants in V.A. Markov’s inequality in LpLp norms

This paper gives the following generalization of Markov’s inequalities ‖P(k)‖p≤(C(p+1)k2)1/p‖Tn(k)‖∞‖P‖p for the kkth derivative of an algebraic polynomial in LpLp norms, where p≥1p≥1. In particular we show that for any k≥3k≥3 the constant CC in the Markov inequality satisfies C≤1223e2.