On the infimum of the absolute value of successive derivatives of a real function defined on a bounded interval

TL;DR

This paper investigates the maximum ratio between the smallest absolute value of a higher derivative of a function and its Lp-norm on a bounded interval, providing insights into the behavior of derivatives relative to the function's norm.

Contribution

It introduces a new analysis of the relationship between higher derivatives and the Lp-norm of functions on bounded intervals, establishing bounds for their ratios.

Findings

Derived bounds for the ratio of derivatives to Lp-norms

Identified extremal functions achieving these bounds

Extended understanding of derivative behavior relative to function norms

Abstract

A study of the greatest possible ratio of the smallest absolute value of a higher derivative of some function, defined on a bounded interval, to the L p-norm of the function.