Boundedness of operators generated by fractional semigroups associated with Schrödinger operators on Campanato type spaces via T1 theorem

Let $${\mathcal {L}}=-\varDelta +V$$ be a Schrödinger operator, where the nonnegative potential V belongs to reverse Hölder class $$B_{q}$$ . By aid of subordinative formula, we estimate regularities fractional heat semigroup, $$\{e^{-t{\mathcal {L}}^{\alpha }}\}_{t>0},$$ associated with {L}}$$ As an application, obtain BMO $$^{\gamma }_{{\mathcal {L}}}$$ -boundedness maximal function, and Littlewood–Paley g-functions via T1 theorem, respectively.