We establish necessary and sufficient conditions on the real- or complex-valued potential defined on for the relativistic Schrödinger operator to be bounded as an operator from the Sobolev space to its dual .
Nous donnons des conditions nécessaires et suffisantes sur le potentiel , défini sur et à valeurs réelles ou complexes, pour que l’opérateur de Schrödinger relativiste soit un opérateur borné de l’espace de Sobolev dans son dual .
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 
@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}, pages = {317--339}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {2}, year = {2004}, doi = {10.5802/aif.2020}, zbl = {02123569}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2020/} }
TY - JOUR AU - Maz'ya, Vladimir AU - Verbitsky, Igor TI - The form boundedness criterion for the relativistic Schrödinger operator JO - Annales de l'Institut Fourier PY - 2004 SP - 317 EP - 339 VL - 54 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2020/ DO - 10.5802/aif.2020 LA - en ID - AIF_2004__54_2_317_0 ER -
%0 Journal Article %A Maz'ya, Vladimir %A Verbitsky, Igor %T The form boundedness criterion for the relativistic Schrödinger operator %J Annales de l'Institut Fourier %D 2004 %P 317-339 %V 54 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2020/ %R 10.5802/aif.2020 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2020/
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