Abstract
We prove a Hardy inequality for fractional powers of a discrete Laplacian, which can be seen as a generalized fractional version of the classical Hardy inequality in Landau (J Lond Math Soc 1:38–39, 1926). Such inequality will be deduced from a ground state representation, following in this way the approach used by Frank, Lieb, and Seiringer in the continuous Euclidean setting.
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Acknowledgements
Ó. C. and L. R. were supported by the grant MTM2015-65888-C4-4-P from Spanish Government. L. R. was also supported by the Basque Government through the BERC 2018–2021 program, by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and through project MTM2017-82160-C2-1-P funded by (AEI/FEDER, UE) and acronym “HAQMEC”, and by a 2017 Leonardo grant for Researchers and Cultural Creators, BBVA Foundation. The Foundation accepts no responsibility for the opinions, statements and contents included in the project and/or the results thereof, which are entirely the responsibility of the authors.
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Ciaurri, Ó., Roncal, L. Hardy’s inequality for the fractional powers of a discrete Laplacian. J Anal 26, 211–225 (2018). https://doi.org/10.1007/s41478-018-0141-2
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DOI: https://doi.org/10.1007/s41478-018-0141-2