We continue the investigation initiated in [Grafakos and Li: Uniform bounds for the bilinear Hilbert transforms, I. Ann. of Math. (2) 159 (2004), 889-933] of uniform bounds for the family of bilinear Hilbert transforms
In this work we show that map into uniformly in the real parameters , satisfying when and . As a corollary we obtain uniform bounds in the range for the 's when .
Cite this article
Xiaochun Li, Uniform Bounds for the Bilinear Hilbert Transforms, II. Rev. Mat. Iberoam. 22 (2006), no. 3, pp. 1069–1126