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