Extrapolation from $A_{\infty}^{\rho,\infty}$, vector-valued inequalities and applications in the Schrödinger settings

Abstract

In this paper, we generalize the A_∞ extrapolation theorem (Cruz-Uribe–Martell–Pérez, Extrapolation from A_∞ weights and applications, J. Funct. Anal. 213 (2004), 412–439) and the A_p extrapolation theorem of Rubio de Francia to Schrödinger settings. In addition, we also establish weighted vector-valued inequalities for Schrödinger-type maximal operators by using weights belonging to $A_{p}^{\rho,\infty }$ which includes A_p. As applications, we establish weighted vector-valued inequalities for some Schrödinger-type operators.