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Equivalence of Sobolev norms involving generalized Hardy operators

Frank, Rupert L. and Merz, Konstantin and Siedentop, Heinz (2018) Equivalence of Sobolev norms involving generalized Hardy operators. . (Unpublished)

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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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Frank, Rupert L.0000-0001-7973-4688
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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Deutsche Forschungsgemeinschaft (DFG)SI 348/15-1
Record Number:CaltechAUTHORS:20190520-135826551
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95610
Deposited By: Tony Diaz
Deposited On:20 May 2019 23:25
Last Modified:03 Oct 2019 21:15

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