论文标题
高维丢失数字集中的加权近似
Weighted approximation in higher-dimensional missing digit sets
论文作者
论文摘要
在本说明中，我们将质量转移原理用于矩形，最近由Wang and Wu（Math。Ann。，2021）获得，以研究“加权$ψ$ - 可相似”点的Hausdorff尺寸，以$ \ MATHBB {r}^d} $。具体而言，我们研究了“丢失数字”集中的加权$ψ$ - 可容纳的点，以$ \ mathbb {r}^{d} $。我们认为的集合是$ \ mathbb {r} $以更高尺寸的cantor型集合的天然概括，例如，在平面中包括四个角式cantor set（或cantor dust），其收缩比$ \ frac {1} {n} {n} {n} $ n \ in \ in \ in \ inthbb in \ natbb {n n} $ {n} $。
In this note, we use the mass transference principle for rectangles, recently obtained by Wang and Wu (Math. Ann., 2021), to study the Hausdorff dimension of sets of "weighted $Ψ$-well-approximable" points in certain self-similar sets in $\mathbb{R}^{d}$. Specifically, we investigate weighted $Ψ$-well-approximable points in "missing digit" sets in $\mathbb{R}^{d}$. The sets we consider are natural generalisations of Cantor-type sets in $\mathbb{R}$ to higher dimensions and include, for example, four corner Cantor sets (or Cantor dust) in the plane with contraction ratio $\frac{1}{n}$ with $n \in \mathbb{N}$.
