Regularity and continuity of commutators of the Hardy-Littlewood maximal function

Let M be the Hardy-Littlewood maximal function and let [b, M] be its corresponding commutator. For 1 < p(1), p(2), p, q < infinity and 1/p = 1/p(1) + 1/p(2), we show that the commutator [b, M] is bounded and continuous from Sobolev space W-s,W-p1(R-d) to Sobolev space W-s,W-p (R-d) for 0 <= s <= 1 when b is an element of W-s,W-p2 (R-d), from Triebel-Lizorkin space F-s(p1,q) (R-d) to F-s(p,q) (R-d) if b is an element of F-s(p2,q) (R-d) and from Besov space B-s(p1,q) (R-d) to B-s(p,q) (R-d) if b is an element of B-s(p2,q) (R-d) and 0 < s < 1.