Vertical Littlewood–Paley functions related to a Schrödinger operator

. In this work we consider the Littlewood–Paley quadratic function associated to the Schr¨odinger operator L = − ∆ + V involving spatial derivatives of the semigroup’s kernel. Under an appropriate reverse-H¨older condition on the potential we show boundedness on weighted L p spaces for 1 < p < p 0 , where p 0 depends on the order of the reverse-H¨older property. Using a subordination formula we extend these results to the corresponding quadratic function associated to the semigroup related to L α , 0 < α < 1.