Peetre's inequality

In mathematics, Peetre's inequality, named after Jaak Peetre, says that for any real number t and any vectors x and y in Rⁿ, the following inequality holds:

$\left( \frac{1+|x|^2}{1+|y|^2} \right)^t \le 2^{|t|} (1+|x-y|^2)^{|t|}.$

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This article incorporates material from Peetre's inequality on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.