Compactness and existence results in weighted Sobolev spaces of radial functions. Part I: compactness

Given two measurable functions (Formula presented.) we define the weighted spaces (Formula presented.) and study the compact embeddings of the radial subspace of (Formula presented.) q are considered. Our results do not require any compatibility between how the potentials V and K behave at the origin and at infinity, and essentially rely on power type estimates of their relative growth, not of the potentials separately. Applications to existence results for nonlinear elliptic problems like (Formula presented.) will be given in a forthcoming paper.