Quantitative boundedness of Littlewood–Paley functions on weighted Lebesgue spaces in the Schrödinger setting

Abstract

Let L:=−Δ+V be the Schrödinger operator on Rn with n≥3, where V is a non-negative potential which belongs to certain reverse Hölder class RHq(Rn) with q∈(n/2,∞). In this article, the authors obtain the quantitative weighted boundedness of Littlewood–Paley functions gL, SL and gL,λ⁎, associated to L, on weighted Lebesgue spaces Lp(w), where w belongs to the class of Muckenhoupt Ap weights adapted to L.