Higher order perturbation estimates in quasi-Banach Schatten spaces through wavelets

Let [Formula: see text]. Let [Formula: see text] and set the Hölder combination [Formula: see text]. Assume further that [Formula: see text] and that for the Hölder combinations of [Formula: see text] to [Formula: see text] and [Formula: see text] to [Formula: see text] we have, [Formula: see text] Then there exists a constant [Formula: see text] such that for every [Formula: see text] with [Formula: see text] we have [Formula: see text] Here [Formula: see text] is the Schatten von Neumann class, [Formula: see text] the homogeneous Besov space, and [Formula: see text] is the multilinear Schur multiplier of the [Formula: see text]-th order divided difference function. In particular, our result holds for [Formula: see text] and any [Formula: see text] with [Formula: see text].