L2 Estimates in Nonlinear Fourier Analysis
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.
KeywordsPseudodifferential Operator Quadratic Estimate Carleson Measure Cancellation Condition Nonlinear Version
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