Marcinkiewicz积分交换子的研究进展

Recent Progress on Commutators of Marcinkiewicz Integral

文章旨在介绍M arc ink iew icz积分交换子的发展研究状况,其中包括笔者近几年对M arc ink iew icz积分交换子的研究成果。主要内容涉及M arc ink iew icz积分交换子在Lp空间、Herz空间、Hardy型空间的有界性和端点情形的弱型LlogL估计,并提出若干有待研究的问题。

This is a survey on the commutators of Marcinkiewicz integrals. The main purpose of this paper is to present some recent progress in this field. The boundedness properties of the commutators of Marcinkiewicz integrals on L^p spaces, Herz spaces, Hardy-type spaces and the weak-type LlogL estimates at the endpoint case are stated. Furthermore, some open problems are posed.