no. 2
The form boundedness criterion for the relativistic Schrödinger operator
[Un critère de bornitude pour l'opérateur de Schrödinger relativiste]
Maz'ya, Vladimir1 ; Verbitsky, Igor
1 Linköping University, Department of Mathematics, Linköping 581-83 (Suède), University of Missouri, Department of Mathematics, Columbia, MO 65211 (USA)
Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 317-339.

Nous donnons des conditions nécessaires et suffisantes sur le potentiel Q, défini sur ℝ 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 (ℝ n ) dans son dual W 2 -1/2 (ℝ n ).

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

DOI : 10.5802/aif.2020
Classification : 35J10, 31C15, 42B15, 46E35
Keywords: relativistic Schrödinger operator, complex-valued potentials, Sobolev spaces
Mot clés : opérateur de Schrödinger relativiste, potentiels à valeurs complexes, espaces de Sobolev

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},
     journal = {Annales de l'Institut Fourier},
     pages = {317--339},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
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Maz'ya, Vladimir; Verbitsky, Igor. The form boundedness criterion for the relativistic Schrödinger operator. Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 317-339. doi : 10.5802/aif.2020. https://aif.centre-mersenne.org/articles/10.5802/aif.2020/

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