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FRACTIONAL SOBOLEV–POINCARÉ AND FRACTIONAL HARDY INEQUALITIES IN UNBOUNDED JOHN DOMAINS

Part of: Inequalities Linear function spaces and their duals

Published online by Cambridge University Press:  20 October 2014

Ritva Hurri-Syrjänen  and
Antti V. Vähäkangas
Ritva Hurri-Syrjänen
Affiliation:
Department of Mathematics and Statistics, Gustaf Hällströmin katu 2b, FI-00014 University of Helsinki, Finland email [email protected]
Antti V. Vähäkangas
Affiliation:
Department of Mathematics and Statistics, Gustaf Hällströmin katu 2b, FI-00014 University of Helsinki, Finland email [email protected]
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Abstract

We prove fractional Sobolev–Poincaré inequalities in unbounded John domains and we characterize fractional Hardy inequalities there.

MSC classification

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Type
Research Article
Information
Mathematika , Volume 61 , Issue 2 , May 2015 , pp. 385 - 401
Copyright
Copyright © University College London 2014 

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References

Dyda, B., A fractional order Hardy inequality. Illinois J. Math. 48 2004, 575–588.CrossRefGoogle Scholar
Dyda, B., Ihnatsyeva, L. and Vähäkangas, A. V., On improved fractional Sobolev–Poincaré inequalities, Preprint, 2013, arXiv:1312.5118.Google Scholar
Dyda, B. and Vähäkangas, A. V., A framework for fractional Hardy inequalities. Ann. Acad. Sci. Fenn. Math. 39 2014, 675–689.CrossRefGoogle Scholar
Dyda, B. and Vähäkangas, A. V., Characterizations for fractional Hardy inequality. Adv. Calc. Var. 2014, http://dx.doi.org/10.1515/acv-2013-0019.Google Scholar
Edmunds, D. E. and Hurri-Syrjänen, R., The improved Hardy inequality. Houston J. Math. 37 2011, 929–937.Google Scholar
Edmunds, D. E., Hurri-Syrjänen, R. and Vähäkangas, A. V., Fractional Hardy-type inequalities in domains with uniformly fat complement. Proc. Amer. Math. Soc. 142 2014, 897–907.CrossRefGoogle Scholar
Franchi, B., Perés, C. and Wheeden, R. L., Self-improving properties of John–Nirenberg and Poincaré inequalities on spaces of homogeneous type. J. Funct. Anal. 153 1998, 109–146.CrossRefGoogle Scholar
Heikkinen, T., Koskela, P. and Tuominen, H., Sobolev-type spaces from generalized Poincaré inequalities. Studia Math. 181 2007, 1–16.CrossRefGoogle Scholar
Hurri-Syrjänen, R., Unbounded Poincaré domains. Ann. Acad. Sci. Fenn. Ser. A I. Math. 17 1992, 409–423.CrossRefGoogle Scholar
Hurri-Syrjänen, R., Marola, N. and Vähäkangas, A. V., Aspects of local to global results. Bull. Lond. Math. Soc. 46(5) 2014, 1032–1042.CrossRefGoogle Scholar
Hurri-Syrjänen, R. and Vähäkangas, A. V., On fractional Poincaré inequalities. J. Anal. Math. 120 2013, 85–104.CrossRefGoogle Scholar
Maz’ya, V., Sobolev Spaces with Applications to Elliptic Partial Differential Equations, 2nd revised and augmented edn. (A Series of Comprehensive Studies in Mathematics 342), Springer (Heidelberg, Dordrecht, London, New York, 2011).CrossRefGoogle Scholar
Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press (Princeton, NJ, 1970).Google Scholar
Väisälä, J., Exhaustions of John domains. Ann. Acad. Sci. Fenn. Ser. A I. Math. 19 1994, 47–57.Google Scholar