Multipliers in Dual Sobolev Spaces and Schrödinger Operators with Distribution Potentials

Abstract

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