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A Carleson type theorem for a Cantor group model of the scattering transform

Camil Muscalu·Terence Tao·Christoph Thiele
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Abstract

We consider a basic $d$-adic model for the scattering transform on the line. We prove $L^2$ bounds for this scattering transform and a weak $L^2$ bound for a Carleson type maximal operator. The latter implies boundedness of $d$-adic models of generalized eigenfunctions of Dirac type operators with potential in $L^2(R)$. We show that this result cannot be obtained by estimating the terms in the natural multilinear expansion of the scattering transform.

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Camil Muscalu, Terence Tao, Christoph Thiele. 2002-05-13. A Carleson type theorem for a Cantor group model of the scattering transform. https://doi.org/10.1088/0951-7715%2F16%2F1%2F314

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