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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 $u d\mu$.
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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