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

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