In mathematics, the Riesz rearrangement inequality, sometimes called Riesz–Sobolev inequality, states that any three non-negative functions
,
and
satisfy the inequality
![{\displaystyle \iint _{\mathbb {R} ^{n}\times \mathbb {R} ^{n}}f(x)g(x-y)h(y)\,dx\,dy\leq \iint _{\mathbb {R} ^{n}\times \mathbb {R} ^{n}}f^{*}(x)g^{*}(x-y)h^{*}(y)\,dx\,dy,}](//wikimedia.org/api/rest_v1/media/math/render/svg/0038213e01806b7df29310d4b474b0daa543107d)
where
,
and
are the symmetric decreasing rearrangements of the functions
,
and
respectively.