Equivalence of Sobolev Norms Involving Generalized Hardy Operators

Frank, Rupert L. ; Merz, Konstantin und Siedentop, Heinz (2021): Equivalence of Sobolev Norms Involving Generalized Hardy Operators. In: International Mathematics Research Notices, Bd. 2021, Nr. 3: S. 2284-2303

Abstract

We consider the fractional Schrodinger operator with Hardy potential and critical or subcritical coupling constant. This operator generates a natural scale of homogeneous Sobolev spaces, which we compare with the ordinary homogeneous Sobolev spaces. As a byproduct, we obtain generalized and reversed Hardy inequalities for this operator. Our results extend those obtained recently for ordinary (non-fractional) Schrodinger operators and have an important application in the treatment of large relativistic atoms.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1073-7928
• Sprache: Englisch