Multipliers in dual Sobolev spaces and Schrödinger operators with distribution potentials (Q1810111)

The goal of this paper is to study the multipliers from the Sobolev space \(H^\alpha_p(\mathbb{R}^n)\) to the dual space \(H_{p'}^{-\alpha}(\mathbb{R}^n)\), where \(\alpha\geq 0\), \(p\geq 1\), and \(p,p'\) are Hölder conjugate indices. Here the authors give a complete description of the spaces of multipliers from \(H_p^\alpha (\mathbb{R}^n)\) to \(H_{p'}^{-\alpha} (\mathbb{R}^n)\) (they denote these spaces by \(M^\alpha_p)\) provided that the condition \(\alpha>n/p\) holds. In the case of \(\alpha\leq p/n\) the authors obtain embedding theorems for Sobolev spaces with negative smoothness indices in the spaces \(M^\alpha_p\). The obtained results are applied to define the Schrödinger operator with distribution potentials.