Evaluation of the One-Dimensional Lp Sobolev Type Inequality

Abstract

This study applies the extended L 2 Sobolev type inequality to the L p Sobolev type inequality using Hölder’s inequality. The sharp constant and best function of the L p Sobolev type inequality are found using a Green function for the nth order ordinary differential equation. The sharp constant is shown to be equal to the L p norm of the Green function and to the pth root of the value of the origin of the best function.