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

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