论文标题
良好的功能，措施和Kleinbock-Tomanov猜想
Good functions, measures, and the Kleinbock-Tomanov conjecture
论文作者
论文摘要
在本文中，我们证明了Kleinbock和Tomanov \ Cite \ Cite [猜想〜fp] {kt}在$ \ mathbb {q} _p^n $上的大型分形测量的双分形措施上。更笼统地，我们在友好措施的Diophantine特性上建立了Kleinbock，Lindenstrauss和Weiss \ cite {Klw}的有影响力结果的$ P $ -ADIC类似物。我们进一步证明了\ cite {kleinbock-exponent}的主要结果之一的$ p $ - adiic类似物，这是由于kleinbock涉及仿射子空间的二磷的继承，这回答了kleinbock的问题。 \ cite {klw}证明中的关键成分之一是$（c，α）$ - 良好函数的结果，其证明至关重要地使用平均值定理。我们的主要技术创新是确定某些功能为$（c，α）$的另一种方法 - 在$ p $ -ADIC设置中良好。我们认为，这一结果将具有独立的利益。
In this paper we prove a conjecture of Kleinbock and Tomanov \cite[Conjecture~FP]{KT} on Diophantine properties of a large class of fractal measures on $\mathbb{Q}_p^n$. More generally, we establish the $p$-adic analogues of the influential results of Kleinbock, Lindenstrauss, and Weiss \cite{KLW} on Diophantine properties of friendly measures. We further prove the $p$-adic analogue of one of the main results in \cite{Kleinbock-exponent} due to Kleinbock concerning Diophantine inheritance of affine subspaces, which answers a question of Kleinbock. One of the key ingredients in the proofs of \cite{KLW} is a result on $(C, α)$-good functions whose proof crucially uses the mean value theorem. Our main technical innovation is an alternative approach to establishing that certain functions are $(C, α)$-good in the $p$-adic setting. We believe this result will be of independent interest.
