WEIGHTED NORM INEQUALITIES FOR SCHRÖDINGER OPERATORS ON VARIABLE LEBESGUE SPACES.

In this work we show that many operators from harmonic analysis associated with the semigroup generated by the Schrödinger operator L = -Δ+V in Rⁿ, where n > 2 and the non-negative potential V belongs to the reverse Hölder class RH_q with q > n/2- such as maximal operators, the Littlewood-Paley function, pseudo-differential operators, singular integrals, and their commutators are bounded on the weighted variable Lebesgue space L^P(.)(w). We do so by applying the theory of weighted norm inequalities and extrapolation. [ABSTRACT FROM AUTHOR]