scholarly journals Almost everywhere convergence and boundedness of cesàro-$\alpha$ ergodic averages

1999 ◽  
Vol 43 (3) ◽  
pp. 592-611 ◽  
Author(s):  
F. J. Martín-Reyes ◽  
M. D. Sarrión Gavilán
Keyword(s):  
Ergodic Averages ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere

Convergence and divergence of ergodic averages

1994 ◽  
Vol 14 (3) ◽  
pp. 515-535 ◽  
Author(s):  
Roger L. Jones ◽  
Mate Wierdl
Keyword(s):  
Ergodic Averages ◽  
Almost Everywhere Convergence ◽  
Large Classes ◽  
Almost Everywhere ◽  
Cesaro Averages ◽  
Convergence And Divergence ◽  
General Method

AbstractIn this paper we consider almost everywhere convergence and divergence properties of various ergodic averages. A general method is given which can be used to construct averages for which a.e. convergence fails, and to show divergence (and in some cases ‘strong sweeping out’) for large classes of ergodic averages. We also show that there are sequences with the gaps between successive terms converging to zero, but such that the Cesaro averages obtained by sampling a flow along these sequences of times converge a.e. for all f∈L1(X).

scholarly journals Pointwise convergence of certain continuous-time double ergodic averages

2021 ◽  
pp. 1-11
Author(s):  
MICHAEL CHRIST ◽  
POLONA DURCIK ◽  
VJEKOSLAV KOVAČ ◽  
JORIS ROOS
Keyword(s):  
Recent Work ◽  
Hilbert Transform ◽  
Continuous Time ◽  
Pointwise Convergence ◽  
Probability Space ◽  
Singular Integrals ◽  
Ergodic Averages ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere ◽  
Multilinear Singular Integrals

Abstract We prove almost everywhere convergence of continuous-time quadratic averages with respect to two commuting $\mathbb {R}$ -actions, coming from a single jointly measurable measure-preserving $\mathbb {R}^2$ -action on a probability space. The key ingredient of the proof comes from recent work on multilinear singular integrals; more specifically, from the study of a curved model for the triangular Hilbert transform.

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