On fractional powers of the Schrödinger operator with a potential singular on manifolds

Sufficient conditions on the degree of summability $p$ are found under which the Sсhrödinger operator with a potential singular on manifolds is a positive operator in Banach spaces $L_p$, and it is also shown that the domains of different degrees of this operator form an interpolation pair. In addition, we establish sufficient conditions on $p$ that ensure that fractional powers $\sigma$, $0< \sigma < 1$ of the operator are bounded from $W_p^{2\sigma}$ to $L_p$.