Let
$\Lambda \subset {\mathbb{R}}^{n}$ be a closed
and discrete set. The vector space consisting of all trigonometric sums whose frequencies belong
to
$\Lambda $ is denoted
by
${\mathcal{T}}_{\Lambda}$. Given an
exponent
$p\in \left[1,\infty \right]$ we
say that
$\Lambda $ is
$p$coherent if there exist
a compact set
$K\subset {\mathbb{R}}^{n}$ and a
continuous function
$\omega $
defined on
${\mathbb{R}}^{n}$ with
values in
$\left[1,\infty \right)$ such
that for every
$P\in {\mathcal{T}}_{\Lambda}$ and
every
$y\in {\mathbb{R}}^{n}$ one has
${\left({\int}_{xy\le 1}P\left(x\right){}^{p}\phantom{\rule{0.3em}{0ex}}dx\right)}^{1\u2215p}\le \omega \left(y\right){\left({\int}_{K}P\left(x\right){}^{p}\phantom{\rule{0.3em}{0ex}}dx\right)}^{1\u2215p}$. Several properties
of
$p$coherent
sets are proved in this essay.
