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Frank, Rupert L. ORCID logoORCID: https://orcid.org/0000-0001-7973-4688; 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

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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.

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