Abstract
In this article we prove an important inequality regarding the Ruelle operator in hyperbolic flows. This was already proven briefly by Mark Pollicott and Richard Sharp in a low dimensional case [Amer. J. Math. 120 (1998), 1019–1042], but we present a clearer proof of the inequality, filling in gaps and explaining the ideas in more detail, and extend the inequality to higher-dimensional flows. This inequality is necessary to prove a proposition about the analyticity of Ruelle zeta functions.