Inequalities for the ergodic maximal function and convergence of the averages in weighted $L^ p$-spaces
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- by F. J. Martín-Reyes PDF
- Trans. Amer. Math. Soc. 296 (1986), 61-82 Request permission
Abstract:
This paper is concerned with the characterization of those positive functions $w$ such that Hopf’s averages associated to an invertible measure preserving transformation $T$ and a positive function $g$ converge almost everywhere for every $f \in {L^p}(w d\mu )$. We also study mean convergence when $g$ satisfies a "doubling condition" over orbits. In order to do this, we first characterize the pairs of positive functions $(u,w)$ such that the ergodic maximal operator associated to $T$ and $g$ is of weak or strong type with respect to the measures $w d\mu$ and $u d\mu$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 296 (1986), 61-82
- MSC: Primary 28D05; Secondary 47A35
- DOI: https://doi.org/10.1090/S0002-9947-1986-0837798-1
- MathSciNet review: 837798