Some notes on $L^{p}$ Bernstein inequality when $0<p<1$

TL;DR

This paper extends the sharp $L^{p}$ Bernstein inequality to the case where $0<p<1$, building on recent results and earlier work by Arestov, for unions of finitely many intervals.

Contribution

It generalizes the $L^{p}$ Bernstein inequality to the case $0<p<1$, providing a broader understanding of polynomial inequalities in this range.

Findings

Extended Bernstein inequality to $0<p<1$

Built on recent asymptotic sharpness results

Connected with earlier work by Arestov

Abstract

Recently, Nagy-To\'okos and Totik-Varga proved an asymptotically sharp $L^{p}$ Bernstein type inequality on union of finitely many intervals. We extend this inequality to the case when the power $p$ is between $0$ and $1$; such sharp Bernstein type inequality was proved first by Arestov.