Weighted norm inequalities for Schrödinger operators on variable Lebesgue spaces

Abstract

In this work we show that many operators from harmonic analysis associated with the semigroup generated by the Schr ̈odinger operator L = −Δ +V in

n , where n > 2 and the

non–negative potential V belongs to the reverse H ̈older class RHq with q > n/2 – such as max- imal operators, the Littlewood–Paley function, pseudo–differential operators, singular integrals,

and their commutators – are bounded on the weighted variable Lebesgue space Lp(·) (w). We do

so by applying the theory of weighted norm inequalities and extrapolation.