The Boundedness For Multilinear Commutator Of Singular Integral Operator With Variable Calderon-zygmund Kernel

In this paper, we mainly study the boundedness of multilinear commutatorsΦ(?) generated by the singular integral operator with variable Calderon-Zygmund kernel and locally integrable functions.First, we prove the sharp function inequality for the multilinear commutatorΦ(?) related to the singular integral operator with variable Calderon-Zygmund kernel. By using the sharp inequality, we obtain the LP-norm inequality for the multilinear commutator.Second, we prove the weighted endpoint estimates for the multilinear commutatorΦ(?) of singular integral with variable Calderon-Zygmund kernel.Furthermore, the boundedness for the multilinear commutatorΦ(?) associated with the singular integral operator with variable Calderon-Zygmund kernel are obtained on Hardy space.Finally, we will study the continuity of multilinear commutatorΦ(?) generated by singular integral with variable Calderon-Zygmund kernel and the functionsθj, where the functionsθj belong to Lipschiz space.