Moment bounds for dependent sequences in smooth Banach spaces

Abstract: We prove a Marcinkiewicz-Zygmund type inequality for random variables taking values in a smooth Banach space. Next, we obtain some sharp concentration inequalities for the empirical measure of ${T, T^2, \cdots, T^n}$, on a class of smooth functions, when $T$ belongs to a class of nonuniformly expanding maps of the unit interval.