Boundedness for Marcinkiewicz integrals associated with Schrödinger operators

Let L = −Δ + V be a Schrödinger operator, where Δ is the Laplacian on ℝn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {R}^{n}$\end{document}, while nonnegative potential V belongs to the reverse Hölder class. In this paper, we will show that Marcinkiewicz integral associated with Schrödinger operator is bounded on BMOL, and from HL1(ℝn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H^{1}_{L}(\mathbb {R}^{n})$\end{document} to L1(ℝn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{1}(\mathbb {R}^{n})$\end{document}.