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In a domain $\Omega\subset \mathbb{R}^{\mathbf{N}}$ we consider a selfadjointoperator $\mathbf{T}=\mathfrak{A}^*P\mathfrak{A} ,$ where $\mathfrak{A}$ is apseudodifferential 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 thesurface measure $\mu_{\Sigma}$ on $\Sigma$. We establish eigenvalue estimatesand asymptotics for this operator. It turns out that the order of theseestimates and asymptotics is independent of the dimension $d$ of the surface.If there are several surfaces, possibly, of different dimensions, as well as anabsolute continuous measure on $\Omega$ the corresponding asymptoticcoefficients add up.

Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case