论文标题
新的$ p $ -adic lipschitz功能和多维汉瑟的引理
A new class of $p$-adic Lipschitz functions and multidimensional Hensel's Lemma
论文作者
论文摘要
在这项工作中，我们在几个变量中研究$ p $ - ad的连续函数，以$ \ mathbb {z} _p $上的值进行值。我们描述了这些功能的正顺式范德，并在几个变量中研究了各种Lipschitz条件，从而推广了Anashin的先前工作。特别是，我们介绍了新的$ P $ -Adic Lipschitz功能，并研究其某些属性。我们还证明了Hensel在这一新功能中的提升引理，从而推广了Yurova和Khrennikov的先前结果。
In this work we study $p$-adic continuous functions in several variables taking values on $\mathbb{Z}_p$. We describe the orthonormal van der Put base of these functions and study various Lipschitz conditions in several variables, generalizing previous work of Anashin. In particular, we introduce a new class of $p$-adic Lipschitz functions and study some of their properties. We also prove a Hensel's lifting lemma for this new class of functions, generalizing previous results of Yurova and Khrennikov.
