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In [[mathematics]], the '''Riesz rearrangement inequality''', sometimes called '''Riesz–Sobolev''' inequality, states that ...>h^* : \mathbb{R}^n \to \mathbb{R}^+</math> are the [[symmetric decreasing rearrangement]]s of the functions <math>f</math>, <math>g</math> and <math>h</math> respe ...

where <math>f^*</math> and <math>g^*</math> are the [[symmetric decreasing rearrangement]]s of <math>f</math> and <math>g</math>, respectively.<ref name=liebloss>{{ </ref><ref name=burchard>{{cite book|title=A Short Course on Rearrangement Inequalities|first=Almut|last=Burchard|author-link=Almut Burchard|url=http://www.math.to ...

...nite-dimensional [[Hilbert space]] and Calkin sequence spaces (also called rearrangement invariant sequence spaces). The correspondence is implemented by mapping a | title=Some matrix inequalities and metrization of matrix space ...

...tion in a [[Sobolev space]] does not increase under [[symmetric decreasing rearrangement]].<ref name=":0" /> The inequality is named after the [[mathematician]]s [[ ...thematics)|function]] <math>u:\R^n\to \R^+,</math>the symmetric decreasing rearrangement <math>u^*:\R^n\to \R^+,</math> is the unique function such that for every < ...

...\Omega)</math>. We denote by <math>f^{*}</math> the [[symmetric decreasing rearrangement]] of nonnegative measurable function f and define it as <math>f^{*}(x):=\in | title = A Short Course on Rearrangement Inequalities ...

...1|page=2|title=On the case of equality in Bobkov's inequality and Gaussian rearrangement|volume=13|journal=Calculus of Variations|doi=10.1007/PL00009921|s2cid=11996 [[Category:Probabilistic inequalities]] ...

...>\boldsymbol {\beta}</math> must satisfy the [[ordered vector space|vector inequalities]] <math> \boldsymbol{b}_\ell \leq \boldsymbol{\beta} \leq \boldsymbol{b}_u< ...e pseudoinverse]]) back into the original expression gives (following some rearrangement) an equation that can be solved as a purely constrained problem in <math>\m ...

...ony Milne|date=2014-04-02|language=en|title=The Euler and Grace-Danielsson inequalities for nested triangles and tetrahedra: A derivation and generalisation using ...og post by [[John C. Baez|John Baez]] in 2014. The comments were lost in a rearrangement of the website, but the central parts were copied into the original blog po ...

...ace (linear algebra)|traces]] of matrices.<ref name="C09">E. Carlen, Trace Inequalities and Quantum Entropy: An Introductory Course, Contemp. Math. 529 (2010) 73–1 which with rearrangement and substitution is Klein's inequality: ...

...course of 15 years Dixmier, aided by a suggestion of Nachman Aronszajn and inequalities proved by Joseph Hersch, developed an example of a non-trivial yet non-norm ...dence]] between two-sided ideals of bounded operators on Hilbert space and rearrangement invariant sequence spaces. Using the spectral characterisation of the [[com ...

...olynomial]], [[Bernstein's theorem on monotone functions]] and [[Bernstein inequalities in probability theory]] *'''[[Nikolay Demyanov]]''', discoverer of [[Demjanov rearrangement]] in [[organic chemistry]] ...

An algebraic rearrangement of this equation allows us to solve for rotational speed: ...rinciple'') is any of a variety of [[Inequality (mathematics)|mathematical inequalities]]<ref name=Sen2014>{{Cite journal |last1 = Sen | first1 = D. | title = The ...