演 讲 人：韩永生教授（美国Auburn大学）
演讲题目：Littlewood-Paley Theory and Hardy Spaces in Multiparameter Analysis（1）
内容摘要：Multiparameter analysis began with Zygmund strong maximal function and Marcinkiewicz multiplier, and continued with Stein, Gundy, Fefferman, Chang and Jouney's works on singular integrals, Hardy and BMO spaces on the product Euclidean space. Multiparameter analysis appeared first implicitly in the work of Phone and Stein when they studied some classes of pseudo-differential and singular integral operators that arise typically in non-coercive boundary-value problems for elliptic equations. The Marcinkiewicz multiplier on the Heisenberg groups was an excellent example of multiparameter singular integrals. Muller-Ricci-Stein proved its boundedness on Lp and introduced flag singular integrals. Very recently, Stein-Yung study the phenomena that arise when one combines the classical pseudo-differential operators with those operators appeared in the subelliptic estimates, and on strongly pseudo-convex domains, They introduced a new pseudo-differential operators which contain the standard isotropic and non-isotropic pseudo-differential operators. They obtained the Lp boundedness and showed that this new class forms an algebra. In this talk, we will describe the Littlewood-Paley theory and the Hardy spaces in multi-parameter analysis. Particularly, we will concentrate on Stein-Yung's work.