Abstract
In this articale, we assert that the best constant of the Sobolev subcritical operator in R is achieved. Moreover we estimate the best constant and the achieved function.Using numerical method, we estimate that the best constant is about 0.7029 as p is large and the minimun value of the best constant is about 0.621073 when p is about 8.055. １. Introduction……………………………………1 ２. Fundamental Lemmas…………………………3 ３. Best Constant of Sobolev Subcritical Operators…13 References……………………………………………….23