Some estimates for multilinear commutators on the weighted Morrey spaces

Purpose: The purpose of this paper is to study the multilinear commutator in weighted Morrey space. Methods: We divide the multilinear commutator into four parts and apply with the methods of weighted Lebesgue space and P´erez and Trujillo-Gonz´alez. Results: Let b = (b1, · · · , bm), bj ∈ BMO(R^n), 1 ≤ j ≤ m; we show that T_b is bounded on weighted Morrey spaces L^p,κ (w), 1 p ∞, 0 κ 1, w ∈ Ap. When p = 1, it is shown that T_b is weak type bounded on weighted Morrey space. Conclusions: We extend the results of the commutator in weighted Morrey space. In particular, for m = 1, this result is also new in the classical commutator.