On the a.s. convergence of the one-sided ergodic Hilbert transform
2009 ◽
Vol 29
(6)
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pp. 1781-1788
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Keyword(s):
AbstractWe show that for T a Dunford–Schwartz operator on a σ-finite measure space (X,Σ,μ) and f∈L1(X,μ), whenever the one-sided ergodic Hilbert transform ∑ n≥1(Tnf/n) converges in norm, it converges μ-a.s. A similar result is obtained for any positive contraction of some fixed Lp(X,Σ,μ), p>1. Applying our result to the case where T is the (unitary) operator induced by a measure-preserving (invertible) transformation, we obtain a positive answer to a question of Gaposhkin.
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1973 ◽
Vol 25
(2)
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pp. 252-260
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Keyword(s):
Keyword(s):
1960 ◽
Vol 97
(2)
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pp. 254-254
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1992 ◽
Vol 53
(1)
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pp. 9-16
1979 ◽
Vol 31
(2)
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pp. 441-447
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Keyword(s):
1977 ◽
Vol 24
(2)
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pp. 129-138
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