实单位球上的面积积分算子

Area Integral Operator on the Real Unit Ball

摘要: 本文通过Carleson boxes或者Tents的方式定义了实单位球上的Carleson测度，并建立了单位球上非切极大函数、Poisson积分和Carleson测度之间的联系。作为一个应用，我们引入一种与中单位球体上非负测度相关的面积积分算子，并用Carleson测度和其他方式刻画了这种使得从到或从到有界的非负测度。

Abstract: In this paper, we introduce Carleson measures on the real unit ball in terms of Carleson boxes or tents, and establish relations among the non-tangential maximal function, Poisson integral and Carleson measures on the real unit ball. As an application, we introduce a certain area integral operator involving a nonnegative measure on the unit ball and characterize the measure in terms of Carleson measure and other forms such that maps from to or from to .