Singular Integrals and Differentiability Properties of Functions
E325281
"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.
All labels observed (3)
How this entity was disambiguated
This entity first appeared as the object of triple T3072659 — 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: Singular Integrals and Differentiability Properties of Functions Context triple: [Annals of Mathematics Studies, hasNotableWork, Singular Integrals and Differentiability Properties of Functions]
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A.
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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B.
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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C.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
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D.
Lezioni di calcolo differenziale assoluto
"Lezioni di calcolo differenziale assoluto" is a foundational mathematical text by Tullio Levi-Civita that systematically develops the theory of absolute differential calculus, now known as tensor calculus, with applications to geometry and physics.
-
E.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
- 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: Singular Integrals and Differentiability Properties of Functions Target entity description: "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.
-
A.
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.
-
B.
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.
-
C.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
-
D.
Lezioni di calcolo differenziale assoluto
"Lezioni di calcolo differenziale assoluto" is a foundational mathematical text by Tullio Levi-Civita that systematically develops the theory of absolute differential calculus, now known as tensor calculus, with applications to geometry and physics.
-
E.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ mathematician ⓘ |
| author |
Elias Stein
ⓘ
surface form:
Elias M. Stein
|
| authorInstanceOf |
Elias Stein
ⓘ
surface form:
Elias M. Stein
|
| contribution |
clarified relationship between singular integrals and differentiability properties of functions
ⓘ
developed modern theory of singular integral operators ⓘ systematized Calderón–Zygmund methods in harmonic analysis ⓘ |
| field |
functional analysis
ⓘ
harmonic analysis ⓘ real analysis ⓘ |
| influenced | modern harmonic analysis ⓘ |
| language | English ⓘ |
| notableFor |
applications to differentiability and regularity theory
ⓘ
rigorous treatment of singular integrals on Lp spaces ⓘ |
| topic |
Calderón–Zygmund theory
ⓘ
surface form:
Calderón–Zygmund decomposition
Calderón–Zygmund theory ⓘ
surface form:
Calderón–Zygmund operators
Calderón–Zygmund theory ⓘ Fourier analysis ⓘ Fourier multipliers ⓘ Hardy–Littlewood maximal function ⓘ
surface form:
Hardy–Littlewood maximal operator
Hilbert transform ⓘ Lebesgue differentiation theorem ⓘ Littlewood–Paley theory ⓘ Lp spaces ⓘ Poisson integral ⓘ Riesz transforms ⓘ Sobolev spaces ⓘ boundedness of operators on Lp ⓘ convolution operators ⓘ differentiability almost everywhere ⓘ differentiability of functions ⓘ differentiation of integrals ⓘ distribution theory ⓘ harmonic extensions ⓘ interpolation of operators ⓘ kernel estimates ⓘ maximal functions ⓘ maximal singular integrals ⓘ measure theory ⓘ singular integral operators ⓘ singular kernels ⓘ tempered distributions ⓘ truncation of singular integrals ⓘ weak-type estimates ⓘ |
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: Singular Integrals and Differentiability Properties of Functions Description of subject: "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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
Annals of Mathematics Studies
→
hasNotableWork
→
Singular Integrals and Differentiability Properties of Functions
ⓘ
Hardy–Littlewood maximal function
→
relatedTo
→
Singular Integrals and Differentiability Properties of Functions
ⓘ
this entity surface form:
Calderón–Zygmund theory
this entity surface form:
Real Analysis: Measure Theory, Integration, and Hilbert Spaces