A new of looking at distributional estimates; applications for the bilinear Hilbert transform.
Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. These distributional estimates show that the square root of the bilinear Hilbert transform is exponentially lntegrable...