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The Individual Weighted Ergodic Theorem for Bounded Besicovitch Sequences
Published online by Cambridge University Press: 20 November 2018
Abstract
Let (X, , μ) be a σ-finite measure space, p fixed, 1 < p < ∞, T a linear operator of Lp(X,μ), {αi} a sequence of complex numbers. If
exists and is finite a.e. we say the individual weighted ergodic theorem holds for T with the weights {αi}
In this paper we show that if {αi} is a bounded Besicovitch sequence and T is a Dunford-Schwartz operator (i.e.: ||T||1≤1, ||T||∞≤1) then the individual weighted ergodic theorem holds for T with the weights {αi}.
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- Copyright © Canadian Mathematical Society 1982
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