Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Calderón–Zygmund decomposition | Statement: [Calderón–Zygmund theory, usesConcept, Calderón–Zygmund decomposition]

Target entity: Calderón–Zygmund decomposition
Context triple: [Calderón–Zygmund theory, usesConcept, Calderón–Zygmund decomposition]

• A. Calderón–Zygmund theory
  Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
• B. 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.
• 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. Jessen’s theorem in harmonic analysis
  Jessen’s theorem in harmonic analysis is a result that provides conditions under which certain trigonometric or Fourier series converge almost everywhere, reflecting Børge Jessen’s contributions to the study of convergence phenomena in harmonic analysis.
• E. Riesz transforms
  Riesz transforms are fundamental singular integral operators in harmonic analysis that generalize the Hilbert transform to higher dimensions and play a key role in studying function spaces and partial differential equations.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Calderón–Zygmund decomposition
Target entity description: The Calderón–Zygmund decomposition is a fundamental tool in harmonic analysis that splits an integrable function into a “good” part with controlled size and a “bad” part localized on sets of small measure to facilitate estimates for singular integral operators.

• A. Calderón–Zygmund theory chosen
  Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
• B. 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.
• 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. Jessen’s theorem in harmonic analysis
  Jessen’s theorem in harmonic analysis is a result that provides conditions under which certain trigonometric or Fourier series converge almost everywhere, reflecting Børge Jessen’s contributions to the study of convergence phenomena in harmonic analysis.
• E. Riesz transforms
  Riesz transforms are fundamental singular integral operators in harmonic analysis that generalize the Hilbert transform to higher dimensions and play a key role in studying function spaces and partial differential equations.
• F. None of above.