Let us consider the class of ``nonvariational uniformly hypoelliptic
operators'':
$$
Lu\equiv\sum_{i,j=1}^{q}a_{ij} (x) X_{i} X_{j} u
$$
where: $X_1,X_2,\ldots,X_q$ is a system of H\"ormander vector
fields in $\mathbb{R}^{n}$ ($n>q$), $\{a_{ij}\}$ is a
$q\times q$ uniformly elliptic matrix, and the functions
$a_{ij} (x)$ are continuous, with a suitable control
on the modulus of continuity. We prove that:
$$
\| X_{i} X_{j} u \|_{BMO(\Omega^{\prime})} \leq
c \left\{\left\|Lu\right\|_{BMO(\Omega)}
+ \left\| u\right\|_{BMO(\Omega)} \right\}
$$
for domains $\Omega^{\prime}\subset\subset\Omega$ that are regular
in a suitable sense. Moreover, the space $BMO$ in the above estimate
can be replaced with a scale of spaces of the kind studied by
Spanne. To get this estimate, several results are proved, regarding
singular and fractional integrals on general spaces of homogeneous
type, in relation with function spaces of $BMO$ type.