L2 Estimates in Nonlinear Fourier Analysis

  • R. Coifman
  • S. Semmes
Conference paper


One of the goals of classical Fourier analysis is to obtain L p estimates for linear operators that commute with translations. The case of p = 2 plays a special role, because of Placherel’s theorem, and because of the availability of methods from the Calderon- Zygmund school for deriving L p estimates from the L 2 case. However, the relevance of Plancherel’s theorem fades swiftly to oblivion when we shift our attention to nonlinear objects. (The Calderon-Zygmund technology does not.) In this paper we present an approach to dealing with nonlinear functionals that commute with translations and which satisfy nonlinear versions of the Calderon-Zygmund conditions.


Pseudodifferential Operator Quadratic Estimate Carleson Measure Cancellation Condition Nonlinear Version 


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  1. [CDM]
    R.R. Coifman, G. David, and Y. Meyer, La solution des conjectures de C alder on, Adv. in Math. 48 (1983), 144–148.MathSciNetMATHCrossRefGoogle Scholar
  2. [CM]
    R.R. Coifman and Y. Meyer, Au-dela des operateurs pseudo-differentiels, Asterisque 57, Societe Mathematique de France, Paris, 1978.Google Scholar
  3. [JL]
    J.L. Journe, Calderon-Zvgmund Operators, Pseudodifferential Operators, and the Cauchv Integral of Calderon, Lecture Notes in Math., Springer-Verlag 999, 1983.Google Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • R. Coifman
    • 1
  • S. Semmes
    • 2
  1. 1.Dept. of MathematicsYale UniversityNew HavenUSA
  2. 2.Dept. of MathematicsRice UniversityHoustonUSA

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