Calderón-Zygmund operators with kernels of Dini’s type on generalized weighted variable exponent Morrey spaces

Let T be a Calderón-Zygmund operator of type ω with ω(t) being nondecreasing and satisfying a kind of Dini’s type condition and let Tb→ be the multilinear commutators of T with BMOm functions. In this paper, we study the boundedness of the operators T and Tb→ on generalized weighted variable exponent Morrey spaces Mp(·),φ(w) with the weight function w belonging to variable Muckenhoupt’s class Ap(·)(Rn). We find the sufficient conditions on the pair (φ1, φ2) with b→ ∈ BMOm(Rn) which ensures the boundedness of the operators T and Tb→ from Mp(·),φ1(w) to Mp(·),φ2(w). © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.