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

Abstract

In this paper, we generalize the $A_\fz$ extrapolation theorem in \cite{cmp} and the $A_p$ extrapolation theorem of Rubio de Francia to Schrödinger settings. In addition, we also establish the weighted vector-valued inequalities for Schrödinger type maximal operators by using weights belonging to $ A_p^{ρ,\tz}$ which includes $A_p$. As their applications, we establish the weighted vector-valued inequalities for some Schödinger type operators and pseudo-differential operators.