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Fractional Hardy-type inequalities in domains with uniformly fat complement


Authors: David E. Edmunds, Ritva Hurri-Syrjänen and Antti V. Vähäkangas
Journal: Proc. Amer. Math. Soc. 142 (2014), 897-907
MSC (2010): Primary 46E35; Secondary 26D10
DOI: https://doi.org/10.1090/S0002-9939-2013-11818-6
Published electronically: November 21, 2013
MathSciNet review: 3148524
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Abstract: We establish fractional Hardy-type inequalities in a bounded
domain with uniformly fat complement. In particular, our results apply in bounded $ C^{\infty }$ domains and Lipschitz domains.


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Additional Information

David E. Edmunds
Affiliation: Department of Mathematics, Pevensey II Building, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom
Email: davideedmunds@aol.com

Ritva Hurri-Syrjänen
Affiliation: Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2, FI-00014 University of Helsinki, Finland
Email: ritva.hurri-syrjanen@helsinki.fi

Antti V. Vähäkangas
Affiliation: Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2, FI-00014 University of Helsinki, Finland
Email: antti.vahakangas@helsinki.fi

DOI: https://doi.org/10.1090/S0002-9939-2013-11818-6
Keywords: Fractional Hardy-type inequality, domain with uniformly fat complement, domain with regular complement, Lipschitz domain, $C^\infty$ domain
Received by editor(s): February 17, 2012
Received by editor(s) in revised form: March 17, 2012, and April 2, 2012
Published electronically: November 21, 2013
Additional Notes: The third author was supported by the Academy of Finland, grants 75166001 and 1134757, and by the Finnish Academy of Science and Letters, Vilho, Yrjö and Kalle Väisälä Foundation
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.