On the integrability of the ergodic hilbert transform for a class of functions with equal absolute values |
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| Authors: | L. Ephremidze |
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| Affiliation: | (1) A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., 380093 Tbilisi, Georgia |
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| Abstract: | ![]()
It is proved that for an arbitrary non-atomic finite measure space with a measure-preserving ergodic transformation there exists an integrable functionf such that the ergodic Hilbert transform of any function equal in absolute values tof is non-integrable. |
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| Keywords: | Ergodic Hilbert transform |
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