V. Markov's problem for monotone polynomials

Abstract

We consider the classical problem of estimating norm of the derivative of algebraic polynomial via the norm of polynomial itself. The corresponding extremal problem for general polynomials in uniform norm was solved by V. Markov. In this note we solve analogous problem for monotone polynomials. As a consequence, we find exact constant in Bernstein inequality for monotone polynomials.

Cited by in corpus (1)

• On the sum of the L1 influences of bounded functions