论文标题
$（α，2α）$ - furstenberg的尺寸的改进限制
An improved bound for the dimension of $(α,2α)$-Furstenberg sets
论文作者
论文摘要
我们表明，给定$α\在（0，1）$中，有一个常数$ c = c（α）> 0 $，以便任何平面$（α，2α）$ - furstenberg set的hausdorff尺寸至少$2α+ c $。这改善了以前的几个范围，特别是扩展了Katz-Tao和Bourgain的结果。我们遵循Katz-Tao方法，并在澄清，简化和/或量化许多步骤的过程中进行了适当的更改。
We show that given $α\in (0, 1)$ there is a constant $c=c(α) > 0$ such that any planar $(α, 2α)$-Furstenberg set has Hausdorff dimension at least $2α+ c$. This improves several previous bounds, in particular extending a result of Katz-Tao and Bourgain. We follow the Katz-Tao approach with suitable changes, along the way clarifying, simplifying and/or quantifying many of the steps.
