On the sharpness of one inequality of different metrics for algebraic polynomials

TL;DR

This paper demonstrates that a known inequality relating different metrics for algebraic polynomials is optimal in terms of order, confirming its fundamental sharpness.

Contribution

It establishes the sharpness of an existing inequality for algebraic polynomials across various metrics, confirming its theoretical optimality.

Findings

The inequality is sharp in the sense of order.

The proof confirms the optimality of the inequality.

The result applies to multiple metrics for algebraic polynomials.

Abstract

We prove that the previously established inequality of different metrics for algebraic polynomials is sharp in the sense of order.