For conjugate exponents $p,q$ and $A,B\ge0$, $AB\le A^p/p+B^q/q$.Suggest a slogan
Let \(1<p,q<\infty\) satisfy \(\frac1p+\frac1q=1\), and let \(A,B\geq0\). Then \[ AB \leq \frac{A^p}{p} + \frac{B^q}{q} . \]
Young's product inequality
PR-BPOH2
PR-BPOH2
Let \(1<p,q<\infty\) satisfy \(\frac1p+\frac1q=1\), and let \(A,B\geq0\). Then \[ AB \leq \frac{A^p}{p} + \frac{B^q}{q} . \]