 Clarkson inequality

ID: clarkson-inequality

For

2 \leq p < \infty

, the Clarkson inequality is

\frac{f + g}{2}_{p}^{p} + \frac{f - g}{2}_{p}^{p} \leq \frac{∥ f ∥ _{p}^{p} + ∥ g ∥ _{p}^{p}}{2} .

It gives the uniform convexity of

L^{p}

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