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arXiv · 2606.22134

On the boundedness for the bilinear quadratic functional given by arbitrary strips

Frédéric Bernicot
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Abstract

This study provides initial results on the boundedness of the (smooth) bilinear quadratic functional defined by an arbitrary collection of disjoint strips. The square function under consideration is a combination between the well-known Rubio de Francia square function from the linear setting with the bilinear Hilbert transform's singularity structure, which involves modulation invariance.

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Frédéric Bernicot. 2026-06-20. On the boundedness for the bilinear quadratic functional given by arbitrary strips. https://arxiv.org/abs/2606.22134

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