Young inequality for convolutions
E412923
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Young's convolution inequality | 2 |
| Hausdorff–Young inequality | 1 |
| Young inequality for convolutions canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4092141 — 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: Young inequality for convolutions Context triple: [Hölder inequality, usedToShow, Young inequality for convolutions]
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A.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
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B.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
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C.
Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
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D.
Hardy–Littlewood maximal function
The Hardy–Littlewood maximal function is a fundamental operator in real analysis and harmonic analysis that controls the local averages of a function and plays a key role in differentiation theorems and singular integral theory.
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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: Young inequality for convolutions Target entity description: 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.
-
A.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
B.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
C.
Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
-
D.
Hardy–Littlewood maximal function
The Hardy–Littlewood maximal function is a fundamental operator in real analysis and harmonic analysis that controls the local averages of a function and plays a key role in differentiation theorems and singular integral theory.
-
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
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical inequality
ⓘ
result in functional analysis ⓘ result in harmonic analysis ⓘ |
| appliesTo |
Lebesgue integrable functions
ⓘ
Lp functions ⓘ |
| category | inequalities in analysis ⓘ |
| conditionOnExponents |
1 + 1/r = 1/p + 1/q
ⓘ
1 ≤ p,q,r ≤ ∞ ⓘ |
| domain |
functions on R^n
ⓘ
functions on locally compact groups ⓘ |
| field |
analysis
ⓘ
functional analysis ⓘ harmonic analysis ⓘ |
| generalizationOf | basic L^1–L^∞ convolution bound ⓘ |
| guarantees | continuity of convolution mapping between Lp spaces ⓘ |
| holdsOn |
R^n with Lebesgue measure
ⓘ
locally compact abelian groups ⓘ |
| implies | boundedness of convolution operator from L^p×L^q to L^r ⓘ |
| involvesConcept |
Hölder inequality
ⓘ
Lebesgue spaces ⓘ
surface form:
Lebesgue space
Lp space ⓘ Minkowski inequality ⓘ convolution ⓘ integrable function ⓘ measure space ⓘ norm inequality ⓘ |
| namedAfter | William Henry Young ⓘ |
| proofUses |
Hölder inequality
ⓘ
Minkowski inequality ⓘ
surface form:
Minkowski integral inequality
|
| relatedTo |
Young inequality for convolutions
self-linksurface differs
ⓘ
surface form:
Hausdorff–Young inequality
Young's inequality ⓘ
surface form:
Young inequality for products
|
| relates |
L^p norm
ⓘ
L^q norm ⓘ L^r norm ⓘ |
| requires |
Fubini's theorem
ⓘ
surface form:
Fubini theorem for integrals
associativity of convolution ⓘ |
| specialCase |
‖f∗g‖_2 ≤ ‖f‖_1 ‖g‖_2
ⓘ
‖f∗g‖_p ≤ ‖f‖_1 ‖g‖_p ⓘ ‖f∗g‖_p ≤ ‖f‖_p ‖g‖_1 ⓘ ‖f∗g‖_∞ ≤ ‖f‖_1 ‖g‖_∞ ⓘ |
| statementForm | ‖f∗g‖_r ≤ ‖f‖_p ‖g‖_q ⓘ |
| usedIn |
Fourier analysis
ⓘ
Sobolev space estimates ⓘ approximate identities ⓘ partial differential equations ⓘ probability theory ⓘ signal processing ⓘ study of heat kernel estimates ⓘ theory of convolution operators ⓘ |
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: Young inequality for convolutions Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
Young inequality for convolutions
→
relatedTo
→
Young inequality for convolutions
self-linksurface differs
ⓘ
this entity surface form:
Hausdorff–Young inequality
this entity surface form:
Young's convolution inequality
this entity surface form:
Young's convolution inequality