Multilinear Calderon-Zygmund operators on Morrey space with non-doubling measures

Under the assumption that mu is a non-negative Radon measure on R(d) which only satisfies some growth condition, the authors proved the multilinear Calderon-Zygmund operators are bounded from M(q1)(p1) (k, mu) x ... x M(qm)(pm) (k, mu) into M(q)(p) (k, mu) for some fixed q(1), ..., q(m) is an element of (1, infinity) and 1/q = 1/q(1) + ... + 1/q(m). Furthermore, the authors established the same bounded estimates for the commutators generated by multilinear Calderon-Zygmund operators and RBMO(mu) functions. Some of the results are also new even when the measure mu is the d-dimensional Lebesgue measure.