The form boundedness criterion for the relativistic Schrödinger operator
Annales de l'Institut Fourier, Volume 54 (2004) no. 2, p. 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 : https://doi.org/10.5802/aif.2020
Classification:  35J10,  31C15,  42B15,  46E35
Keywords: relativistic Schrödinger operator, complex-valued potentials, Sobolev spaces
@article{AIF_2004__54_2_317_0,
     author = {Maz'ya, Vladimir and Verbitsky, Igor},
     title = {The form boundedness criterion for the relativistic Schr\"odinger operator},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {2},
     year = {2004},
     pages = {317-339},
     doi = {10.5802/aif.2020},
     zbl = {02123569},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_2_317_0}
}
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/item/AIF_2004__54_2_317_0/

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