Resumen de Vertical Littlewood–Paley functions related to a Schrödinger operator

Bruno Bongioanni, Eleonor O. Harboure , Pablo Quijano

• 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 Lp spaces for 1 < p < p0, where p0 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 Lα, 0 < α < 1.