Commutators of maximal operator and sharp maximal operator onlocal Morrey-Lorentz spaces

In this paper, we study the boundedness of the maximal commutator operator M b , the commutators of the maximal operator [b, M ] and the commutators of the sharp maximal operator [b, M ] in the local Morrey-Lorentz spaces M loc p,q; (R n ).We give necessary and sufficient conditions for the boundedness of the operators M b , [b, M ] and [b, M ] on local Morrey-Lorentz spaces M loc p,q; (R n ) when b belongs to BM O(R n ) spaces, whereby some new characterizations for certain subclasses of BM O(R n ) spaces are obtained.