Hardy–Littlewood inequality
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In mathematical analysis, the Hardy–Littlewood inequality, named after G. H. Hardy and John Edensor Littlewood, states that if and are nonnegative measurable real functions vanishing at infinity that are defined on -dimensional Euclidean space , then
where and are the symmetric decreasing rearrangements of and , respectively.[1][2]
The decreasing rearrangement of is defined via the property that for all the two super-level sets
- and
have the same volume (-dimensional Lebesgue measure) and is a ball in centered at , i.e. it has maximal symmetry.