Conditions for the existence of measurable and integrable solutions of the cohomology equation on a measure space are deduced. They follow from the study of the ergodic structure corresponding to some families of bidimensional linear difference equations. Results valid for the non-measure-preserving case are also obtained
@article{bwmeta1.element.bwnjournal-article-smv138i2p121bwm,
author = {Ana Alonso and Jialin Hong and Rafael Obaya},
title = {Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, 0 < p < $\infty$},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {121-134},
zbl = {0951.28010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv138i2p121bwm}
}
Alonso, Ana; Hong, Jialin; Obaya, Rafael. Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, 0 < p < ∞. Studia Mathematica, Tome 141 (2000) pp. 121-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv138i2p121bwm/
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