  We consider the pure Yang-Mills relativistic quantum field theory in an
imaginary time functional integral formulation. The gauge group is taken to be
$\mathcal G = \mathrm U(N)$. We use a lattice ultraviolet regularization,
starting with the model defined on a finite hypercubic lattice $\Lambda\subset
a\mathbb Z^d$, $d = 2,3,4$, with lattice spacing $a\in (0,1]$ and $L\in\mathbb
N$ sites on a side. The Wilson partition function is used where the action is a
sum over four lattice bond variables of gauge-invariant plaquette (lattice
minimal squares) actions with a prefactor $a^{d-4}/g^2$, where we take the
gauge coupling $g\in(0,g_0^2]$, $0<g_0<\infty$. In a recent paper, for free
boundary conditions, we proved that a normalized model partition function
satisfies thermodynamic and ultraviolet stable stability bounds. Here, we
extend the stability bounds to the Yang-Mills model with periodic boundary
conditions, with constants which are also independent of $L$, $a$, $g$.
Furthermore, we also consider a normalized generating functional for the
correlations of $r\in\mathbb N$ gauge-invariant plaquette fields. Using
periodic boundary conditions and the multireflection method, we then prove that
this generating functional is bounded, with a bound that is independent of $L$,
$a$, $g$ and the location and orientation of the $r$ plaquette fields. The
bounds factorize and each factor is a single-bond variable, single-plaquette
partition function. The number of factors is, up to boundary corrections, the
number of non-temporal lattice bonds, such as $(d-1)L^d$. A new global
quadratic upper bound in the gluon fields is proved for the Wilson plaquette
action.
