Peetre's inequality

In mathematics, Peetre's inequality, named after Jaak Peetre, says that for any real number ${\displaystyle t}$ and any vectors ${\displaystyle x}$ and ${\displaystyle y}$ in ${\displaystyle \mathbb {R} ^{n},}$ the following inequality holds:

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

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

See also

• List of inequalities

References

• Chazarain, J.; Piriou, A. (2011), Introduction to the Theory of Linear Partial Differential Equations, Studies in Mathematics and its Applications, Elsevier, p. 90, ISBN 9780080875354.
• Ruzhansky, Michael; Turunen, Ville (2009), Pseudo-Differential Operators and Symmetries: Background Analysis and Advanced Topics, Pseudo-Differential Operators, Theory and Applications, vol. 2, Springer, p. 321, ISBN 9783764385132.
• Saint Raymond, Xavier (1991), Elementary Introduction to the Theory of Pseudodifferential Operators, Studies in Advanced Mathematics, vol. 3, CRC Press, p. 21, ISBN 9780849371585.

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