Frank, Rupert L. and Merz, Konstantin and Siedentop, Heinz (2021) Equivalence of Sobolev Norms Involving Generalized Hardy Operators. International Mathematics Research Notices, 2021 (3). pp. 2284-2303. ISSN 1073-7928. doi:10.1093/imrn/rnz135. https://resolver.caltech.edu/CaltechAUTHORS:20190520-135826551
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Abstract
We consider the fractional Schrödinger 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) Schrödinger operators and have an important application in the treatment of large relativistic atoms.
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| Additional Information: | © The Author(s) 2019. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). Received: 24 July 2018; Revision received: 12 March 2019; Accepted: 17 May 2019; Published: 09 July 2019. The authors are very grateful to an anonymous referee for many helpful remarks and suggestions. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [grant SI 348/15-1 to H.S. and EXC-2111 390814868 to R.L.F., K.M., H.S.] and the U.S. National Science Foundation [grant DMS-1363432 to R.L.F.]. | |||||||||
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| Issue or Number: | 3 | |||||||||
| DOI: | 10.1093/imrn/rnz135 | |||||||||
| Record Number: | CaltechAUTHORS:20190520-135826551 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190520-135826551 | |||||||||
| Official Citation: | Rupert L Frank, Konstantin Merz, Heinz Siedentop, Equivalence of Sobolev Norms Involving Generalized Hardy Operators, International Mathematics Research Notices, Volume 2021, Issue 3, February 2021, Pages 2284–2303, https://doi.org/10.1093/imrn/rnz135 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 95610 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 20 May 2019 23:25 | |||||||||
| Last Modified: | 13 Apr 2021 22:31 |
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