Weighted weak type inequalities for the ergodic maximal function and the pointwise ergodic theorem
A. de la Torre, F. Martín-Reyes (1987)
Studia Mathematica
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Displaying similar documents to “On pointwise ergodic theorems for positive operators”
Weighted weak type inequalities for the ergodic maximal function and the pointwise ergodic theorem
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Convergence of the averages and finiteness of ergodic power funtions in weighted L spaces.
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Let (X, F, μ) be a finite measure space. Let T: X → X be a measure preserving transformation and let Af denote the average of Tf, k = 0, ..., n. Given a real positive function v on X, we prove that {Af} converges in the a.e. sense for every f in L(v dμ) if and only if inf v(Tx) > 0 a.e., and the same condition is equivalent to the finiteness of a related ergodic power function Pf for every f in L(v dμ). We apply this result to characterize, being T null-preserving, the finite...
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Diego Gallardo (1987)
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