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Zbl 1126.35011
Maz'ya, Vladimir; Verbitsky, Igor
(Verbitskiĭ, I. E.)
The form boundedness criterion for the relativistic Schrödinger operator. (English)
[J] Ann. Inst. Fourier 54, No. 2, 317-339 (2004). ISSN 0373-0956; ISSN 1777-5310/e

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

MSC 2000:: *35Q75 PDE in relativity
35J10 Schroedinger operator
46E35 Sobolev spaces and generalizations
81Q10 Selfadjoint operator theory in quantum theory
47F05 Partial differential operators

Keywords: relativistic Schrödinger operator; complex-valued potentials; Sobolev spaces

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