Abstract

The study of boundedness of Hormander multipliers and its multilinear generalization is an important topic in harmonic analysis. In this talk we discuss initial boundedness of multilinear Hormander multipliers of Calder\'on-Torchinsky type, i.e., the $L^2\times\cdots\times L^2$ boundedness of them. For this purpose, we establish a substitute of the Plancherel identity in the multilinear setting, which turns out to be useful in obtaining the boundedness of many other multilinear operators.