Riesz rearrangement inequality
E747350
The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Riesz rearrangement inequality canonical | 1 |
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical inequality
ⓘ
result in mathematical analysis ⓘ |
| appliesTo |
functions on R^n
ⓘ
integrals over Euclidean space ⓘ |
| assumes | nonnegative functions ⓘ |
| category | inequalities involving rearrangements of functions ⓘ |
| characterizes | maximizers of certain integral functionals ⓘ |
| compares |
integral of product of functions
ⓘ
integral of product of symmetric decreasing rearrangements ⓘ |
| concerns | rearrangement-invariant bounds ⓘ |
| domain | Euclidean spaces R^n ⓘ |
| ensures | integral does not increase under symmetric decreasing rearrangement ⓘ |
| field |
functional analysis
ⓘ
mathematical analysis ⓘ measure theory ⓘ real analysis ⓘ |
| generalizes | Hardy–Littlewood rearrangement inequality NERFINISHED ⓘ |
| hasConsequence |
sharp constants in functional inequalities
ⓘ
symmetrization techniques in analysis ⓘ |
| holdsFor | Lebesgue measurable functions ⓘ |
| implies | extremal configurations are radially symmetric decreasing ⓘ |
| involves |
nonnegative measurable functions
ⓘ
radially symmetric decreasing functions ⓘ symmetric decreasing rearrangements ⓘ |
| namedAfter | Frigyes Riesz NERFINISHED ⓘ |
| provedBy | Frigyes Riesz NERFINISHED ⓘ |
| provides | optimal bound for integrals of products of functions ⓘ |
| relatedTo |
Brunn–Minkowski inequality
NERFINISHED
ⓘ
Sobolev inequalities NERFINISHED ⓘ isoperimetric inequalities ⓘ |
| statesInequality | ∫ f(x) g(x−y) h(y) dx dy ≤ ∫ f*(x) g*(x−y) h*(y) dx dy ⓘ |
| timePeriod | 20th century ⓘ |
| type | integral inequality ⓘ |
| usedIn |
calculus of variations
ⓘ
concentration inequalities ⓘ geometric analysis ⓘ partial differential equations ⓘ potential theory ⓘ |
| usesConcept |
Hardy–Littlewood rearrangement inequality
NERFINISHED
ⓘ
equimeasurable functions ⓘ level sets of functions ⓘ radial symmetry ⓘ symmetric decreasing rearrangement ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.