Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
E542636
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5709654 — 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: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals Context triple: [Elias Stein, notableWork, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals]
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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.
-
B.
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.
-
C.
Littlewood–Paley theory
Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
-
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.
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.
- 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: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals Target entity description: "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
-
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.
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.
-
C.
Littlewood–Paley theory
Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
-
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.
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.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
graduate-level textbook
ⓘ
harmonic analysis textbook ⓘ mathematics textbook ⓘ |
| audience |
graduate students in mathematics
ⓘ
researchers in harmonic analysis ⓘ |
| author | Elias M. Stein NERFINISHED ⓘ |
| contains |
detailed proofs of major theorems in harmonic analysis
ⓘ
exercises for each chapter ⓘ |
| contribution |
standard reference in harmonic analysis
ⓘ
systematic development of modern real-variable harmonic analysis ⓘ |
| emphasis |
orthogonality methods
ⓘ
oscillatory integral methods ⓘ real-variable techniques ⓘ |
| field |
harmonic analysis
ⓘ
real-variable methods in analysis ⓘ |
| focus |
Euclidean harmonic analysis
ⓘ
Lp spaces ⓘ operator bounds on function spaces ⓘ |
| language | English ⓘ |
| level | graduate ⓘ |
| prerequisite |
basic functional analysis
ⓘ
measure theory ⓘ real analysis ⓘ |
| publisher | Princeton University Press NERFINISHED ⓘ |
| relatedWork |
Fourier Analysis: An Introduction
NERFINISHED
ⓘ
Singular Integrals and Differentiability Properties of Functions NERFINISHED ⓘ |
| series | Princeton Mathematical Series NERFINISHED ⓘ |
| subject |
BMO (bounded mean oscillation)
ⓘ
Calderón–Zygmund theory NERFINISHED ⓘ Carleson-type operators ⓘ Fourier multipliers ⓘ Fourier transform on Euclidean spaces ⓘ Hardy spaces NERFINISHED ⓘ Littlewood–Paley theory NERFINISHED ⓘ Radon transforms ⓘ interpolation of operators ⓘ maximal functions ⓘ oscillatory integral estimates ⓘ oscillatory integrals ⓘ restriction theorems in Fourier analysis ⓘ singular integrals ⓘ square functions ⓘ weighted norm inequalities ⓘ |
| usedAs | graduate course textbook ⓘ |
How these facts were elicited
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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: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals Description of subject: "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Elias Stein
→
notableWork
→
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
ⓘ