Weighted Remez- and Nikolskii-Type Inequalities on a Quasismooth Curve

TL;DR

This paper proves precise weighted inequalities of Remez and Nikolskii types for algebraic polynomials on quasismooth curves in the complex plane, advancing understanding of polynomial behavior in complex analysis.

Contribution

It establishes sharp weighted Remez- and Nikolskii-type inequalities for polynomials on quasismooth curves, a novel setting in complex analysis.

Findings

Sharp weighted inequalities are established for algebraic polynomials.

Results apply to quasismooth curves in the complex plane.

The inequalities are optimal in the weighted setting.

Abstract

We establish sharp $L_p,1\le p<\infty$ weighted Remez- and Nikolskii-type inequalities for algebraic polynomials considered on a quasismooth (in the sense of Lavrentiev) curve in the complex plane.