On solvability of the cohomology equation in function spaces
Volume 156 / 2003
Studia Mathematica 156 (2003), 277-293
MSC: 37A20, 28D05, 47A35.
DOI: 10.4064/sm156-3-5
Abstract
Let $T$ be an endomorphism of a probability measure space $({\mit\Omega },{\cal A},\mu )$, and $f$ be a real-valued measurable function on ${\mit\Omega }$. We consider the cohomology equation $f=h\circ T-h$. 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.
