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arXiv · 2603.20173

The shifted bilinear Hilbert transform

Lars Becker·Polona Durcik
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Abstract

We prove $L^p$ estimates for the shifted bilinear Hilbert transform, with a polylogarithmic bound in the size of the shift. As applications, we obtain $r$-variation estimates for bilinear ergodic averages in the sharp range $r > 2$, a sharp bilinear H\"ormander multiplier theorem, and a $\log$-Dini theorem for bilinear singular integrals.

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Lars Becker, Polona Durcik. 2026-03-20. The shifted bilinear Hilbert transform. https://arxiv.org/abs/2603.20173

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