Boundedness of operators generated by fractional semigroups associated with Schr\"odinger operators on Campanato type spaces via $T1$ theorem

Let $\mathcal{L}=-\mathrm{\Delta }+V$ be a Schr"{o}dinger operator, where the nonnegative potential $V$ belongs to the reverse H"{o}lder class $B_q$. By the aid of the subordinative formula, we estimate the regularities of the fractional heat semigroup, $\{e^{-t{\mathcal{L}}^{\alpha }}{\}}_{t>0},$ associated with $\mathcal{L}$. As an application, we obtain the $BM{O}_{\mathcal{L}}^{\gamma }$-boundedness of the maximal function, and the Littlewood-Paley $g$-functions associated with $\mathcal{L}$ via $T1$ theorem, respectively.