Weighted inequalities for variation operators associated with fractional Schrödinger semigroups

Let -tL^α>0 be the fractional Schrödinger semigroup associated with $L=-Δ+V$, where V is a non-negatvie potential belonging to the reverse Hölder class. In this paper, we establish weighted boundedness properties of the variation operator related to -tL^α>0, including weighted Lᵖ-Lq quantitative inequalities and mixed weak-type inequalities.