There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model: we prove the estimate uniformly for a discrete family of model operators for the bilinear Hilbert transform.
Cite this article
Christoph Thiele, A uniform estimate for quartile operators. Rev. Mat. Iberoam. 18 (2002), no. 1, pp. 115–134DOI 10.4171/RMI/313