A maximal estimate for the non-linear Fourier transform

Alexei Poltoratski

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arXiv · 2608.24606

A maximal estimate for the non-linear Fourier transform

Alexei Poltoratski

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Abstract

We discuss estimates for the maximal operator associated with the non-linear Fourier transform of an $L^2$-function on the half-line. For potentials with bounded dyadic $L^1$ masses we prove weak-type maximal and maximal fluctuation estimates on the sets where the spectral densities are bounded away from zero and three classical maximal functions of the spectral data are uniformly small; such sets exhaust almost all of the real line as the parameters of their definition relax.

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Alexei Poltoratski. 2026-08-25. A maximal estimate for the non-linear Fourier transform. https://arxiv.org/abs/2608.24606

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