Abstract
In this paper we obtain (almost) optimal results concerning randomly weighted one-sided ergodic Hilbert transforms. Given an iid sequence of centered random variables (Xn) in L log L, we show that there exists a universal set . The method applies to powers along subsequences with ‘small’ growth and when considering Dunford–Schwartz operators instead of pointwise transformation. If the (Xn) are symmetric, but only in L log log L, we obtain a slightly weaker result.
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