A new class of $p$-adic Lipschitz functions and multidimensional Hensel's Lemma

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.