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 (2)
| Label | Occurrences |
|---|---|
| Lieb’s theorem on Gaussian kernels | 1 |
| Riesz rearrangement inequality canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8640760 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Riesz rearrangement inequality Context triple: [Frigyes Riesz, knownFor, Riesz rearrangement inequality]
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A.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
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B.
Gagliardo–Nirenberg interpolation inequalities
The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
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C.
Korn inequality
Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
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D.
Young inequality for convolutions
Young inequality for convolutions is a fundamental result in analysis that provides norm bounds for the convolution of functions in Lebesgue spaces, relating the L^p norms of the factors to the L^r norm of their convolution.
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E.
Poincaré inequality
The Poincaré inequality is a fundamental result in functional analysis and partial differential equations that bounds the average oscillation of a function by the size of its gradient, playing a key role in Sobolev space theory and the study of elliptic problems.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Riesz rearrangement inequality Target entity description: 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.
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A.
Riesz–Thorin interpolation theorem
The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
-
B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
C.
Gagliardo–Nirenberg interpolation inequalities
The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
-
D.
Korn inequality
Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
-
E.
Young inequality for convolutions
Young inequality for convolutions is a fundamental result in analysis that provides norm bounds for the convolution of functions in Lebesgue spaces, relating the L^p norms of the factors to the L^r norm of their convolution.
- F. None of above. chosen
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 ⓘ |
| 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 ⓘ |
| provedBy | Frigyes Riesz ⓘ |
| provides | optimal bound for integrals of products of functions ⓘ |
| relatedTo |
Brunn–Minkowski inequality
ⓘ
Sobolev inequalities ⓘ
linked to:
Sobolev inequality
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
ⓘ
equimeasurable functions ⓘ level sets of functions ⓘ radial symmetry ⓘ symmetric decreasing rearrangement ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Riesz rearrangement inequality Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Riesz rearrangement inequality