REGULARITY OF COMMUTATORS OF THE BILINEAR MAXIMAL OPERATOR

We introduce and study the regularity properties of the commutator of the bilinear maximal operator and the bilinear maximal commutator. We establish some new bounds for the weak gradient of the above commutators. We also obtain the boundedness and continuity of the above commutators on the Triebel–Lizorkin spaces and Besov spaces.