  In a domain $\Omega\subset \mathbb{R}^{\mathbf{N}}$ we consider a selfadjoint
operator $\mathbf{T}=\mathfrak{A}^*P\mathfrak{A} ,$ where $\mathfrak{A}$ is a
pseudodifferential operator of order $-l=-\mathbf{N}/2$ and $P=V\mu_{\Sigma}$
is a singular signed measure in $\Omega$ concentrated on a Lipschitz surface
$\Sigma$ of dimension $d<\mathbf{N}$, absolutely continuous with respect to the
surface measure $\mu_{\Sigma}$ on $\Sigma$. We establish eigenvalue estimates
and asymptotics for this operator. It turns out that the order of these
estimates and asymptotics is independent of the dimension $d$ of the surface.
If there are several surfaces, possibly, of different dimensions, as well as an
absolute continuous measure on $\Omega$ the corresponding asymptotic
coefficients add up.
