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The form boundedness criterion for the relativistic Schrödinger operator. (English) Zbl 1126.35011
Summary: We establish necessary and sufficient conditions on the real- or complex-valued potential \(Q\) defined on \({\mathbb R}^n\) for the relativistic Schrödinger operator \(\sqrt{-\Delta} + Q\) to be bounded as an operator from the Sobolev space \(W^{1/2}_2 ({\mathbb R}^n)\) to its dual \(W^{-1/2}_2 ({\mathbb R}^n)\).

MSC:
35Q75 PDEs in connection with relativity and gravitational theory
35J10 Schrödinger operator, Schrödinger equation
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47F05 General theory of partial differential operators
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