Singular integral operator with rough kernel and its commutator on Bourgain–Morrey spaces

Let [Formula: see text] be a homogeneous function of degree zero on the unit sphere [Formula: see text] satisfying the zero-mean condition and belonging to [Formula: see text] for some [Formula: see text]. In this paper, we establish the boundedness of the singular integral operator [Formula: see text] with kernel [Formula: see text] on Bourgain–Morrey space [Formula: see text], and we also consider its related maximal operator [Formula: see text]. Suppose [Formula: see text], the commutator [Formula: see text] generated by the function [Formula: see text] and the operator [Formula: see text] is investigated as well. We further prove that [Formula: see text] is the sufficient condition for the boundedness of the commutator [Formula: see text] on Bourgain–Morrey space [Formula: see text].