Multipliers in Dual Sobolev Spaces and Schrödinger Operators with Distribution Potentials

Certain sufficient conditions for functions to be embedded in the space of multipliers from the Sobolev space $H^\alpha _p({\mathbb R}^n)$ to the dual space $H^{-\alpha }_{p'}({\mathbb R}^n)$ are obtained in the present paper. In the case $\alpha >n/p$ a criterion is found, i.e., a precise description of these spaces of multipliers is given. The obtained results are applied to define the Schödinger operator with distribution potentials.