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 ${\mathbb{ℝ}}^n,$ the following inequality holds: $${\left(\frac{1+|x{|}^2}{1+|y{|}^2}\right)}^t\le 2^{|t|}(1+|x-y{|}^2{)}^{|t|}.$$

The inequality was proved by J. Peetre in 1959 and has founds applications in functional analysis and Sobolev spaces.

See also

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References

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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.

External links

• Planetmath.org: Peetre's inequality