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Equivalence of Sobolev Norms Involving Generalized Hardy Operators

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1093/imrn/rnz135DOIArticle
https://arxiv.org/abs/1807.09027arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
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.].
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SI 348/15-1
Deutsche Forschungsgemeinschaft (DFG)EXC-2111 390814868
NSFDMS-1363432
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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