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| In mathematics, '''Peetre's inequality,''' named after [[Jaak Peetre]], says that for any [[real number]] ''t'' and any [[Vector space|vector]]s ''x'' and ''y'' in '''R'''<sup>n</sup>, the following inequality holds:
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| :<math> \left( \frac{1+|x|^2}{1+|y|^2} \right)^t \le 2^{|t|} (1+|x-y|^2)^{|t|}.</math>
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| ==References==
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| *{{citation|title=Introduction to the Theory of Linear Partial Differential Equations|series=Studies in Mathematics and its Applications|first1=J.|last1=Chazarain|first2=A.|last2=Piriou|publisher=Elsevier|year=2011|isbn=9780080875354|page=90|url=http://books.google.com/books?id=Gh9XeWnOzagC&pg=PA90}}.
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| *{{citation|title=Pseudo-Differential Operators and Symmetries: Background Analysis and Advanced Topics|volume=2|series=Pseudo-Differential Operators, Theory and Applications|first1=Michael|last1=Ruzhansky|first2=Ville|last2=Turunen|publisher=Springer|year=2009|isbn=9783764385132|page=321|url=http://books.google.com/books?id=DDpz_MfxZrUC&pg=PA321}}.
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| *{{citation|title=Elementary Introduction to the Theory of Pseudodifferential Operators|volume=3|series=Studies in Advanced Mathematics|first=Xavier|last=Saint Raymond|publisher=CRC Press|year=1991|isbn=9780849371585|page=21|url=http://books.google.com/books?id=kD5ZCJDIg4oC&pg=PA21}}.
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| {{PlanetMath attribution|id=4681|title=Peetre's inequality}}
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| {{mathanalysis-stub}}
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| [[Category:Linear algebra]]
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| [[Category:Inequalities]]
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.mw-body, mtext {
font-family: Latin Modern Roman;
}
math {
font-family: Latin Modern Math;
}