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

Abstract

Recently, Nagy-Toókos 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.