Boundedness of variation operators and oscillation operators for certain semigroups

In this paper, we study the boundedness of variation operators and oscillation operators for certain semigroups. As applications, this theory can be applied to various settings such as Schrödinger operators, degenerate Schrödinger operators on RnRn and Schrödinger operators on Heisenberg groups and connected and simply connected nilpotent Lie groups.