On the Integrability of the Ergodic Hilbert Transform for A Class of Functions with Equal Absolute Values
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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 function f such that the ergodic Hilbert transform of any function equal in absolute values to f is non-integrable.
1993 ◽
Vol 47
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pp. 119-126
2009 ◽
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pp. 1781-1788
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1973 ◽
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pp. 252-260
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1960 ◽
Vol 97
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pp. 254-254
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1992 ◽
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pp. 9-16
1979 ◽
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pp. 441-447
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1977 ◽
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pp. 129-138
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