Clarkson inequality
= Clarkson inequality
{c}
{wiki=Clarkson's_inequalities}
For $2\leq p<\infty$, the Clarkson inequality is
$$
\left\lVert\frac{f+g}{2}\right\rVert_p^p
+\left\lVert\frac{f-g}{2}\right\rVert_p^p
\leq\frac{\lVert f\rVert_p^p+\lVert g\rVert_p^p}{2}.
$$
It gives the uniform convexity of $L^p$.
= Banach spaces
{c}
{synonym}