Boundedness and compactness characterizations of Riesz transform commutators on Morrey spaces in the Bessel setting

Abstract

Let [Formula: see text] and [Formula: see text] be the Bessel operator on [Formula: see text]. In this paper, the authors show that [Formula: see text] (or [Formula: see text], respectively) if and only if the Riesz transform commutator [Formula: see text] is bounded (or compact, respectively) on Morrey spaces [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text]. A weak factorization theorem for functions belonging to the Hardy space [Formula: see text] in the sense of Coifman–Rochberg–Weiss in Bessel setting, via [Formula: see text] and its adjoint, is also obtained.