On the regular decomposition of the inverse gravimetric problem in non-\(L^2\) spaces

The paper deals with the inverse gravimetric problem generalizing a classical decomposition of mass distributions into a harmonic component and another component that produces a zero external field. After a review and an extension of the well-known \(L^2\) theory, mass distributions in \(L^p\) and in \(H^{-s,2}\) are considered and proved to undergo an analogous decomposition. Examples will make the theory easier to grasp. Conclusions follow.