Another Proof of the Existence of the Ergodic Hilbert Transform

DOI10.2307/2045106zbMath0521.28014OpenAlexW4250678598MaRDI QIDQ3671428

Karl E. Petersen

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/2045106

zbMATH Keywords

measure-preserving transformationdiscrete Hilbert transformergodic Hilbert transform

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Ergodic theory of linear operators (47A35) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (6)

Oscillation and variation for singular integrals in higher dimensions ⋮ On the Ergodic Hilbert Transform for Lamperti Operators ⋮ On convergence of oscillatory ergodic Hilbert transforms ⋮ Pointwise convergence theorems in \(L_ 2\) over a von Neumann algebra ⋮ The Spectral Measure and Hilbert Transform of a Measure-Preserving Transformation ⋮ On the Almost Everywhere Existence of the Ergodic Hilbert Transform

Cites Work

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• The maximal ergodic Hilbert transform with weights
• The ergodic theorem
• A dominated ergodic estimate for $L_{p}$ spaces with weights
• An analog of the Marcinkiewicz integral in ergodic theory
• ERGODIC THEORY AND TRANSLATION-INVARIANT OPERATORS
• Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform
• A note on the Hilbert transform

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