The full range of uniform bounds for the bilinear Hilbert transform

Gennady Uraltsev, Michał Warchalski

We prove uniform uniform $L^p$ bounds for the family of bilinear Hilbert transforms $\mathrm{BHT}_β [f_1, f_2] (x) := \mathrm{p.v.} \int_{\mathbb{R}} f_1 (x - t) f_2 (x + βt) \fr…