关于双边的Young不等式和一个逆定理

On a Two-sided Young luequality and a Converse Theorem

本文将经典的W.H.Young单边不等式扩充成为双边不等式,并证明了一条类似Takahashi的逆定理。文末举了几个简单例子,以说明双边不等式的应用。

The classical inequality of W. H Young provides a best possible lower bound for the Sum of two integrals with reciprocal functions as integrands. In this note, a kind of best Possible upper bound is given, and a converse theorem similar to T. Takahashi's is Proved. Finally a few examples are mentioned which may indicate the usefulness of the two-sided inequality.