Generalized Nikolskii's property and asymptotic exponent in Markov's inequality

TL;DR

This paper introduces an asymptotic Markov's exponent, proves its equality with the classical exponent for many norms, and derives a lower bound for the optimal exponent in Markov's inequality for norms with Nikolskii's property.

Contribution

It establishes the equivalence of asymptotic and classical Markov's exponents for broad norm classes and provides bounds for the optimal exponent in Markov's inequality.

Findings

Asymptotic Markov's exponent equals Markov's exponent for many norms.

Derived a lower bound for the optimal exponent in Markov's inequality.

Extended the understanding of Nikolskii's property in the context of Markov's inequality.

Abstract

We introduce an asymptotic Markov's exponent and show that it is equal to Markov's exponent for a wide class of norms. As a consequence we obtain a lower bound for the optimal exponent in Markov's inequality considered with the norms possessing Nikolskii type property.