John–Nirenberg inequality
E890446
The John–Nirenberg inequality is a fundamental result in harmonic analysis that characterizes functions of bounded mean oscillation (BMO) by showing their oscillations have exponentially decaying distribution.
All labels observed (4)
| Label | Occurrences |
|---|---|
| John–Nirenberg inequality canonical | 2 |
| John–Nirenberg inequality on spaces of homogeneous type | 1 |
| dyadic John–Nirenberg inequality | 1 |
| weighted John–Nirenberg inequality | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10881125 — 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: John–Nirenberg inequality Context triple: [Fritz John, notableWork, John–Nirenberg inequality]
-
A.
Fefferman–Phong inequality
The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
-
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.
-
C.
Sobolev inequality
The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
-
D.
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.
-
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: John–Nirenberg inequality Target entity description: The John–Nirenberg inequality is a fundamental result in harmonic analysis that characterizes functions of bounded mean oscillation (BMO) by showing their oscillations have exponentially decaying distribution.
-
A.
Fefferman–Phong inequality
The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
-
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.
-
C.
Sobolev inequality
The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
-
D.
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.
-
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 (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical inequality
ⓘ
result in harmonic analysis ⓘ |
| abbreviation | JN inequality ⓘ |
| appliesTo | locally integrable functions ⓘ |
| assumes | finite BMO seminorm ⓘ |
| characterizes | functions of bounded mean oscillation ⓘ |
| conclusion | tail of oscillation decays exponentially in λ ⓘ |
| describes | exponential decay of distribution of oscillations ⓘ |
| domain |
functions on cubes in ℝⁿ
ⓘ
functions on ℝⁿ ⓘ |
| field |
harmonic analysis
ⓘ
real analysis ⓘ |
| generalizationOf | weak-type inequalities for mean oscillation ⓘ |
| hasForm | P(|f(x)−f_Q|>λ) ≤ C·exp(−cλ/∥f∥_{BMO}) ⓘ |
| hasVariant |
John–Nirenberg inequality on spaces of homogeneous type
ⓘ
linked to:
John–Nirenberg inequality
dyadic John–Nirenberg inequality ⓘ
linked to:
John–Nirenberg inequality
weighted John–Nirenberg inequality ⓘ
linked to:
John–Nirenberg inequality
|
| implies | exponential integrability of BMO functions ⓘ |
| involves |
Lebesgue measure
ⓘ
mean oscillation over cubes ⓘ probabilistic tail estimates ⓘ |
| mathematicsSubjectClassification |
42B35
ⓘ
46E30 ⓘ |
| namedAfter |
Fritz John
ⓘ
Louis Nirenberg ⓘ |
| publishedIn | Communications on Pure and Applied Mathematics ⓘ |
| quantifies | distribution of |f−f_Q| over a cube ⓘ |
| relatedConcept |
BMO space
ⓘ
Calderón–Zygmund theory ⓘ Hardy space ⓘ bounded mean oscillation ⓘ singular integral operators ⓘ |
| relatedTo |
Gehring lemma
ⓘ
reverse Hölder inequalities ⓘ |
| shows |
BMO functions are exponentially integrable locally
ⓘ
oscillations of BMO functions are rare at large size ⓘ |
| strengthens | Chebyshev-type estimates for BMO ⓘ |
| type | local inequality ⓘ |
| usedFor |
embedding results for BMO
ⓘ
equivalence of BMO norms ⓘ estimates for singular integrals ⓘ regularity theory of PDEs ⓘ showing BMO is larger than L^∞ ⓘ |
| usedIn |
Fefferman–Stein theory of Hardy spaces
ⓘ
regularity of solutions to elliptic equations ⓘ regularity of solutions to parabolic equations ⓘ theory of Muckenhoupt A_p weights ⓘ |
| yearProved | 1961 ⓘ |
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: John–Nirenberg inequality Description of subject: The John–Nirenberg inequality is a fundamental result in harmonic analysis that characterizes functions of bounded mean oscillation (BMO) by showing their oscillations have exponentially decaying distribution.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: John–Nirenberg inequality
linked to: John–Nirenberg inequality
linked to: John–Nirenberg inequality