The form boundedness criterion for the relativistic Schrödinger operator
Annales de l'Institut Fourier, Volume 54 (2004) no. 2, pp. 317-339.

We establish necessary and sufficient conditions on the real- or complex-valued potential Q defined on n for the relativistic Schrödinger operator -Δ+Q to be bounded as an operator from the Sobolev space W 2 1/2 ( n ) to its dual W 2 -1/2 ( n ).

Nous donnons des conditions nécessaires et suffisantes sur le potentiel Q, défini sur n et à valeurs réelles ou complexes, pour que l’opérateur de Schrödinger relativiste -Δ+Q soit un opérateur borné de l’espace de Sobolev W 2 1/2 ( n ) dans son dual W 2 -1/2 ( n ).

DOI: 10.5802/aif.2020
Classification: 35J10,  31C15,  42B15,  46E35
Keywords: relativistic Schrödinger operator, complex-valued potentials, Sobolev spaces
Maz'ya, Vladimir 1; Verbitsky, Igor 

1 Linköping University, Department of Mathematics, Linköping 581-83 (Suède), University of Missouri, Department of Mathematics, Columbia, MO 65211 (USA)
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     title = {The form boundedness criterion for the relativistic {Schr\"odinger} operator},
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Maz'ya, Vladimir; Verbitsky, Igor. The form boundedness criterion for the relativistic Schrödinger operator. Annales de l'Institut Fourier, Volume 54 (2004) no. 2, pp. 317-339. doi : 10.5802/aif.2020. http://www.numdam.org/articles/10.5802/aif.2020/

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