Frank, Rupert L. and Merz, Konstantin and Siedentop, Heinz (2018) Equivalence of Sobolev norms involving generalized Hardy operators. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190520-135826551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: | Report or Paper (Discussion Paper) | ||||||
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| Additional Information: | © 2018 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Deutsche Forschungsgemeinschaft grant SI 348/15-1 (R.L.F., K.M., H.S.) and U.S. National Science Foundation grant DMS-1363432 (R.L.F.) are acknowledged. | ||||||
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| Record Number: | CaltechAUTHORS:20190520-135826551 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190520-135826551 | ||||||
| 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: | 03 Oct 2019 21:15 |
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