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
ⓘ
linked to:
Elias Stein
|
| 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 ⓘ |
| relatedWork |
Fourier Analysis: An Introduction
ⓘ
Singular Integrals and Differentiability Properties of Functions ⓘ |
| series | Princeton Mathematical Series ⓘ |
| subject |
BMO (bounded mean oscillation)
ⓘ
Calderón–Zygmund theory ⓘ Carleson-type operators ⓘ Fourier multipliers ⓘ Fourier transform on Euclidean spaces ⓘ Hardy spaces ⓘ
linked to:
Hardy space
Littlewood–Paley theory ⓘ 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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
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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
ⓘ