Let T be an endomorphism of a probability measure space (Ω,𝓐,μ), and f be a real-valued measurable function on Ω. We consider the cohomology equation f = h ∘ T - h. Conditions for the existence of real-valued measurable solutions h in some function spaces are deduced. The results obtained generalize and improve a recent result of Alonso, Hong and Obaya.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-5,
author = {Ryotaro Sato},
title = {On solvability of the cohomology equation in function spaces},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {277-293},
zbl = {1017.37003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-5}
}
Ryotaro Sato. On solvability of the cohomology equation in function spaces. Studia Mathematica, Tome 157 (2003) pp. 277-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-5/