论文标题
抽象的Hardy-Littlewood最大不平等
Abstract Hardy-Littlewood Maximal Inequality
论文作者
论文摘要
在本说明中，介绍了Vitali的两个抽象版本，涵盖引理的抽象版本是一个抽象的硬木极限不平等，概括了弱类型（1,1）最大功能不平等，与任何外部度量相关联，并且引入了集合上的一个子集。当且仅当一个特殊的数值常数称为Hardy-Littelwood Maximal常数是有限的时，不等式就会（有效地）满足。给出了这一常数有限的两个普遍条件，并且在同质空间中的（中心）球的家族，欧几里得空间中的二元立方体家族，同质树中可接受的梯形家族的二元组家族以及均质树中的二二二分方家族，以及calderón-calderón-zygmund家族（轴+b）还提供了一个非常简单的应用程序，以查找有关经典力学中质量密度的一些非平凡估计。
In this note besides two abstract versions of the Vitali Covering Lemma an abstract Hardy-Littlewood Maximal Inequality, generalizing weak type (1,1) maximal function inequality, associated to any outer measure and a family of subsets on a set is introduced. The inequality is (effectively) satisfied if and only if a special numerical constant called Hardy-Littelwood maximal constant is finite. Two general sufficient conditions for the finiteness of this constant are given and upper bounds for this constant associated to the family of (centered) balls in homogeneous spaces, family of dyadic cubes in Euclidean spaces, family of admissible trapezoids in homogeneous trees, and family of Calderón-Zygmund sets in (ax+b)-group, are considered. Also a very simple application to find some nontrivial estimates about mass density in Classical Mechanics is given.
