BV spaces and the perimeters related to Schrödinger operators with inverse-square potentials and applications to the rank-one theorem

For a ? ? ( d 2 1 ) and ? = + 4 , let H ? | x ˜ be two Schrödinger operators with inverse-square potentials. In this paper, on the domain ? ? R ? { 0 } -BV space B V related to are introduced, respectively. We investigate series of basic properties . Furthermore, we prove that -restricted BV functions can characterized equivalently via their subgraphs. As applications, derive rank-one theorem for functions.