On Fractional Powers of the Schrödinger Operator with a Potential Singular on Manifolds

In this paper, the sufficient conditions on summability degree p are found under which the Schrödinger operator with a potential, being singular on manifolds, is a positive one in Banach spaces Lp. It is also demonstrated that the domains of various degrees on this operator form an interpolation pair. In addition to this, the sufficient conditions on p are established which ensure that fractional powers σ, 0 < σ < 1, of this operator are bounded from $$W_{p}^{{2\sigma }}$$ to Lp.

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