Multipliers in dual Sobolev spaces and Schrodinger 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)(R-n) to the dual space H-p'(-alpha)(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 Schrodinger operator with distribution potentials.