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Laws of large numbers with rates and the one-sided ergodic Hilbert transform

2003
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Illinois Journal of Mathematics
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Let T be a power-bounded operator on Lp(µ), 1 < p < ∞. We use a sublinear growth condition on the norms { n k=1 T k f p} to obtain for f the pointwise ergodic theorem with rate, as well as a.e. convergence of the one-sided ergodic Hilbert transform. For µ finite and T a positive contraction, we give a sufficient condition for the a.e. convergence of the "rotated one-sided Hilbert transform"; the result holds also for p = 1 when T is ergodic with T 1 = 1. Our methods apply to norm-bounded

doi:10.1215/ijm/1258138088
fatcat:dmrpc37uzraylpcpttzkzyjc4m