Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 675-689

A FRAMEWORK FOR FRACTIONAL HARDY INEQUALITIES

Bartlomiej Dyda and Antti V. Vähäkangas

University of Bielefeld, Faculty of Mathematics
Postfach 10 01 31, D-33501 Bielefeld, Germany; dyda 'at' math.uni-bielefeld.de, and Wroclaw University of Technology, Institute of Mathematics and Computer Science
Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland; bdyda 'at' pwr.wroc.pl

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; antti.vahakangas 'at' helsinki.fi

Abstract. We provide a general framework for fractional Hardy inequalities. Our framework covers, for instance, fractional inequalities related to the Dirichlet forms of some Lévy processes, and weighted fractional inequalities on irregular open sets.

2010 Mathematics Subject Classification: Primary 26D15, 46E35, 31C25, 26A12.

Key words: Fractional Hardy inequality, fractional Laplacian, regularly varying function, Assouad dimension, uniform fatness, irregular domain.

Reference to this article: B. Dyda and A.V. Vähäkangas: A framework for fractional Hardy inequalities. Ann. Acad. Sci. Fenn. Math. 39 (2014), 675-689.

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doi:10.5186/aasfm.2014.3943