Peetre's inequality
From HandWiki
In mathematics, Peetre's inequality, named after Jaak Peetre, says that for any real number [math]\displaystyle{ t }[/math] and any vectors [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] in [math]\displaystyle{ \Reals^n, }[/math] the following inequality holds: [math]\displaystyle{ \left(\frac{1+|x|^2}{1+|y|^2}\right)^t ~\leq~ 2^{|t|} (1+|x-y|^2)^{|t|}. }[/math]
The inequality was proved by J. Peetre in 1959 and has founds applications in functional analysis and Sobolev spaces.
See also
- List of inequalities – None
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, https://books.google.com/books?id=Gh9XeWnOzagC&pg=PA90.
- Ruzhansky, Michael; Turunen, Ville (2009), Pseudo-Differential Operators and Symmetries: Background Analysis and Advanced Topics, Pseudo-Differential Operators, Theory and Applications, 2, Springer, p. 321, ISBN 9783764385132, https://books.google.com/books?id=DDpz_MfxZrUC&pg=PA321.
- Saint Raymond, Xavier (1991), Elementary Introduction to the Theory of Pseudodifferential Operators, Studies in Advanced Mathematics, 3, CRC Press, p. 21, ISBN 9780849371585, https://books.google.com/books?id=kD5ZCJDIg4oC&pg=PA21.
External links
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