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 to the ergodic Hilbert transform.
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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 σ-finite measure space.
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