Equivalence of Sobolev Norms Involving Generalized Hardy Operators

Frank, Rupert L. ; Merz, Konstantin and Siedentop, Heinz (2021): Equivalence of Sobolev Norms Involving Generalized Hardy Operators. In: International Mathematics Research Notices, Vol. 2021, No. 3: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1073-7928
• Language: English