PROPERTIES OF THE MAXIMAL OPERATORS ASSOCIATED WITH BASES OF RECTANGLES IN $\mathbb{R}^3$
PROPERTIES OF THE MAXIMAL OPERATORS ASSOCIATED WITH BASES OF RECTANGLES IN $\mathbb{R}^3$
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$mathbb{R}^3$ 中与矩形底相关的最大算子的性质
DOI：
10.1017/s0013091506001180
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发表时间：
2008
影响因子：
0.7
通讯作者：
A. Stokolos
中科院分区：
文献类型：
--
作者：
A. Stokolos
本文试图在更一般的索里亚基的框架内理解与三维矩形基（t，1/t，s）有关的极大算子现象. Escheren-Marcinkiewicz-Zygmund定理意味着与索里亚基相关联的极大算子连续地将$L\log^2L$映射到$L^{1，\infty}$。我们给出一个简单的几何条件，保证$L\log^2L$类不能扩大。证明发展了作者的方法以前应用在二维的情况下，是有关定理的科尔多瓦，索里亚和Fridman和Pipher。
Abstract This paper is an attempt to understand a phenomenon of maximal operators associated with bases of three-dimensional rectangles of dimensions $(t,1/t,s)$ within a framework of more general Soria bases. The Jessen–Marcinkiewicz–Zygmund Theorem implies that the maximal operator associated with a Soria basis continuously maps $L\log^2L$ into $L^{1,\infty}$. We give a simple geometric condition that guarantees that the $L\log^2L$ class cannot be enlarged. The proof develops the author's methods applied previously in the two-dimensional case and is related to theorems of Córdoba, Soria and Fefferman and Pipher.