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We study fluctuations of ergodic averages generated by actions of amenablegroups. In the setting of an abstract ergodic theorem for locally compactsecond countable amenable groups acting on uniformly convex Banach spaces, wededuce a highly uniform bound on the number of fluctuations of the ergodicaverage for a class of F{\o}lner sequences satisfying an analogue ofLindenstrauss's temperedness condition. Equivalently, we deduce a uniform boundon the number of fluctuations over long distances for arbitrary F{\o}lnersequences. As a corollary, these results imply associated bounds for acontinuous action of an amenable group on a $\sigma$-finite $L^{p}$ space with$p\in(1,\infty)$.

Fluctuation bounds for ergodic averages of amenable groups on uniformly convex Banach spaces