Inversion and characterization of some potentials with the densities in $L^p$ in the non-elliptic case

We construct the inversion of generalized Strichartz potentials with singularities of the kernels on a finite union of spheres in $\mathbb R^n$ with densities from space $L^p$, $1\leq p\leq 2$ and Hardy space $H^1$ in the non-elliptic case, when its symbols degenerate on a set of zero measure in $\mathbb R^n$. We also give the description of these potentials in terms of the inverting constructions.