  This document comes as supplementary material of the paper Stability in
Gagliardo-Nirenberg inequalities by the same authors. It is intended to state a
number of classical or elementary statements concerning constants and
inequalities for which we are not aware of existing published material or
expressions detailed enough for our purpose. We claim no originality on the
theoretical results and rely on standard methods in most cases, except that we
keep track of the constants and provide constructive estimates.
