On convergence of oscillatory ergodic Hilbert transforms
On convergence of oscillatory ergodic Hilbert transforms
We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound.The latter imply a range of quantitative weighted inequalities, which are new.As an application, we prove the following ergodic theorem: let p(t) be a Hardy field function which grows "super-linearly" and stays "sufficiently …