Commutators of Bilinear θ-Type Calderon-Zygmund Operators on Morrey Spaces Over Non-Homogeneous Spaces

The aim of this paper is to establish the boundedness of the commutator [b(1), b(2), T-theta], which generated by the bilinear theta-type Calderon-Zygmund operators T-theta and the functions b(1),b(2)is an element of(RBMO) over tilde(mu), on non-homogeneous metric measure space satisfying the so-called geometrically doubling and the upper doubling conditions. Under the assumption that the dominating function lambda satisfies the epsilon-weak reverse doubling conditions, the author proves that the commutator [b(1), b(2), T-theta] is bounded from the Lebesgue space L-p(mu) into the product of Lebesgue space L-p1(mu)xL(p2)(mu) with 1/p=1/p(1)+1/p(2)((1 < p, p(1), p(2) < infinity). Furthermore, the boundedness of the commutator [b(1), b(2), T-theta] on Morrey space M-p(q) (mu) is also obtained, where 1 < q <= p < infinity.