Abstract
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.
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References
R.R. Coifman, G. David, and Y. Meyer, La solution des conjectures de C alder on, Adv. in Math. 48 (1983), 144–148.
R.R. Coifman and Y. Meyer, Au-dela des operateurs pseudo-differentiels, Asterisque 57, Societe Mathematique de France, Paris, 1978.
J.L. Journe, Calderon-Zvgmund Operators, Pseudodifferential Operators, and the Cauchv Integral of Calderon, Lecture Notes in Math., Springer-Verlag 999, 1983.
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© 1991 Springer-Verlag Tokyo
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Coifman, R., Semmes, S. (1991). L 2 Estimates in Nonlinear Fourier Analysis. In: Igari, S. (eds) ICM-90 Satellite Conference Proceedings. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68168-7_7
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DOI: https://doi.org/10.1007/978-4-431-68168-7_7
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-70084-5
Online ISBN: 978-4-431-68168-7
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