The shifted bilinear Hilbert transform
Abstract
We prove Lp 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 -Dini theorem for bilinear singular integrals.
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