二叉树上Box条件与Carleson条件的比较
A comparison of box and Carleson conditions on bi-trees
摘要：
本文给出了一个在某些子二叉树上满足盒条件但在这些子二叉树上不满足Carleson条件的测度的例子。这可以看作是Carleson型双权双参数嵌入的一个反例。我们的反例对于简单树是不可能的。在简单树的情况下，盒子条件、Carleson条件和两个权嵌入都是等价的。在最后一节中，我们证明了双参数箱条件蕴含并矢矩形的双参数容性估计。
英文摘要：
In this note we give an example of measure satisfying the box condition on certain sub-bi-trees (see below) but not satisfying Carleson condition on those sub-bi-trees. This can be considered as a certain counterexample for two weight bi-parameter embedding of Carleson type. Our type of counterexample is impossible for a simple tree. In the case of a simple tree, the box condition, Carleson condition and two weight embedding are all equivalent. In the last section we show that bi-parameter box condition implies the bi-parameter capacitary estimate for dyadic rectangles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
