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

Let $mathcal{L}=-Delta+V$ 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, ${e^{-tmathcal{L}^{alpha}}}_{t>0},$ associated with $mathcal{L}$. As an application, we obtain the $BMO^{gamma}_{mathcal{L}}$-boundedness of the maximal function, and the Littlewood-Paley $g$-functions associated with $mathcal{L}$ via $T1$ theorem, respectively.