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:

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

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.

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