  Let E be a field of characteristic p. In a previous paper of ours, we defined
and studied super-H\"older vectors in certain E-linear representations of Z_p.
In the present paper, we define and study super-H\"older vectors in certain
E-linear representations of a general p-adic Lie group. We then consider
certain p-adic Lie extensions K_\infty / K of a p-adic field K, and compute the
super-H\"older vectors in the tilt of K_\infty. We show that these
super-H\"older vectors are the perfection of the field of norms of K_\infty /
K. By specializing to the case of a Lubin-Tate extension, we are able to
recover E((Y)) inside the Y-adic completion of its perfection, seen as a valued
E-vector space endowed with the action of O_K^\times given by the endomorphisms
of the corresponding Lubin-Tate group.

Number Theory