On THE REGULARITY FOR MULTILINEAR PSEUDO-DIFFERENTIAL OPERATORS (Women in Mathematics)

Abstract

In this talk we study a Hormander type estimates about the multilinear pseudo-differential operators associated with a symbol. The symbol classes can be classified by the derivative conditions concerning both space and frequency variables. We firstly introduce known results about these operators when the symbol is independent of the space variable. We nextly extend the derivative conditions of the symbol to more general ones. Especially, we only assume at most the first time of the differentiability of the symbol with respect to the space variable. Under these weakened conditions, we establish the mapping properties of these multilinear operators on the product Hardy spaces. This is based on the joint work with Yaryong Heo and Chan Woo Yang ([1, 2]).