Inequalities for the ergodic maximal function and convergence of the averages in weighted -spaces
Author:
F. J. Martín-Reyes
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
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Abstract | References | Similar Articles | Additional Information
Abstract: This paper is concerned with the characterization of those positive functions such that Hopf's averages associated to an invertible measure preserving transformation
and a positive function
converge almost everywhere for every
. We also study mean convergence when
satisfies a "doubling condition" over orbits. In order to do this, we first characterize the pairs of positive functions
such that the ergodic maximal operator associated to
and
is of weak or strong type with respect to the measures
and
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1986-0837798-1
Keywords:
Ergodic maximal function,
mean convergence,
almost everywhere convergence,
weighted inequalities,
Hopf's averages
Article copyright:
© Copyright 1986
American Mathematical Society