Commutators and localization on the Drury–Arveson space

Let f be a multiplier for the Drury–Arveson space of the unit ball, and let ζ1,…,ζn denote the coordinate functions. We show that for each 1⩽i⩽n, the commutator belongs to the Schatten class Cp, p>2n. This leads to a localization result for multipliers.