The Stein–Weiss theorem for the ergodic Hilbert transform
Volume 165 / 2004
Studia Mathematica 165 (2004), 61-71
MSC: 28D10, 42A50.
DOI: 10.4064/sm165-1-5
Abstract
The Stein–Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of $E$ depends only on the measure of $E$ is generalized for the ergodic Hilbert transform in the case of a one-parameter flow of measure-preserving transformations on a $\sigma $-finite measure space.
