Title: The boundedness of multilinear Calderon-Zygmund operators on weighted and variable spaces.

Abstract: In this talk, we will establish the boundedness of the above operators from a product of weighted Hardy spaces into a weighted Hardy space or weighted Lebesgue space. Our work extends a result of Stromberg and Torchinsky for linear operators to multilinear settings. We will also discuss a useful extrapolation tool that allows us to make further extension of the previous result into variable Hardy spaces.