New classes of Lp-spaces
E547407
"New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| New classes of Lp-spaces canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5790563 — 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: New classes of Lp-spaces Context triple: [Jean Bourgain, notableWork, New classes of Lp-spaces]
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A.
Orlicz spaces
Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
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B.
Lebesgue spaces
Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability theory.
-
C.
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.
-
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.
Sobolev spaces
Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational 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: New classes of Lp-spaces Target entity description: "New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
-
A.
Orlicz spaces
Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
-
B.
Lebesgue spaces
Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability theory.
-
C.
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.
-
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.
Sobolev spaces
Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
- F. None of above. chosen
Statements (33)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical work
ⓘ
research article ⓘ work in functional analysis ⓘ |
| areaOfInfluence |
geometry of Banach spaces
ⓘ
modern Banach space theory ⓘ theory of Lp spaces ⓘ |
| author | Jean Bourgain ⓘ |
| contribution |
advances the theory of Lp spaces in functional analysis
ⓘ
introduces new Banach space structures within Lp spaces ⓘ provides examples of Banach spaces with novel structural properties ⓘ studies geometric properties of Lp-based Banach spaces ⓘ |
| field |
Banach space theory
ⓘ
linked to:
Banach spaces
Lp spaces ⓘ functional analysis ⓘ |
| hasAuthor | Jean Bourgain ⓘ |
| hasAuthorNationality | Belgian ⓘ |
| hasImpactOn |
classification of Banach spaces
ⓘ
construction of counterexamples in functional analysis ⓘ subsequent research on exotic Banach spaces ⓘ |
| language | English ⓘ |
| mainSubject |
Banach spaces
ⓘ
Lp-space structure ⓘ |
| namedAfter | Lp spaces ⓘ |
| relatedTo |
Jean Bourgain's work in Banach space geometry
ⓘ
Jean Bourgain's work in harmonic analysis ⓘ |
| studies |
geometric aspects of Banach spaces
ⓘ
isomorphic classification problems in Lp spaces ⓘ structure of Lp spaces as Banach spaces ⓘ |
| typeOfWork | theoretical mathematics ⓘ |
| usesConcept |
Banach space geometry
ⓘ
Lp norms ⓘ linear operators on Banach spaces ⓘ normed vector spaces ⓘ |
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: New classes of Lp-spaces Description of subject: "New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.