The Boundedness Of Multilinear Singular Integral Operator With Variable Calderón-Zygmund Kernel

In this paper, we mainly study the boundedness of the multilinear integral operator generated by the singular integral operator with variable Calderon-Zygmund kernel T and locally integrable functions.The content of this paper is divided into five parts.In the first part of this paper,we briefly introduce the background of the paper and their significance in theory and practice, we also introduce some signs, definitions and lemmas.In the second part, we prove the weighted boundedness for the multilinear singular integral operators with variable Calderon-Zygmund kernel generated by the singular integral operator with variable Calderon-Zygmund kernel T and BMO functions on L~p and Morrey spaces.In the third part,the boundedness for the multilinear singular integral operators with variable Calderon-Zygmund kernel generated by the singular integral operator with variable Calderon-Zygmund kernel T and BMO functions on Hardy and Herz type Hardy spaces are obtained.In the fourth part of this paper,we prove the continuity for the multilinear operators generated by the singular integral operators with variable Calderon-Zygmund kernel and Lipschitz functions on some Hardy and Herz-type spaces.Finally, we obtain the weighted endpoint estimates for the multilinear singular integral operators with variable Calderon-Zygmund kernel on Hardy and Herz type Hardy spaces.