Riesz transforms, fractional power and functional calculus of Schrödinger operators on weighted \(L^p\)-spaces
The Schrödinger operator \(-\Delta+V^{+}-V^{-}\) on the weighted Lebesgue space \(L^p(\mathbb{R}^N, w\,dx)\), where \(N\geq 3\) and \(w\) is a weight in some Muckenhoupt class, is considered in the paper. The author studies the boundedness of Riesz transform type operators \(\nabla A^{-1/2}\) and \(|V|^{1/2}A^{-1/2}\) on \(L^p(\mathbb{R}^N, wdx)\). The results extend those of \textit{P. Auscher} and \textit{B. Ben Ali} [Ann. Inst. Fourier 57, No.~6, 1975--2013 (2007; Zbl 1161.35003)], \textit{The Anh Bui} [Differ. Integral Equ. 23, No.~9--10, 811--826 (2010; Zbl 1240.42034)], \textit{J. Assaad} and \textit{E. M. Ouhabaz} [J. Geom. Anal. 22, No.~4, 1108--1136 (2012; Zbl 1259.58006)].
scientific article; zbMATH DE number 6156117