  This article generalizes the results of [J. Math. Anal. Appl. 512 (2022),
Article No. 126075], which presented a theory of distributions (generalized
functions) with a singular curve contained in the domain of the test functions.
In this present article we construct a theory of distributions in
$\mathbb{R}^n$ with a ``thick submanifold'', that is, a new theory of thick
distributions in $\mathbb{R}^n$ whose domain contains a submanifold on which
test functions may be singular.
