Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 757-770

ITERATED LOG-SCALE ORLICZ-HARDY INEQUALITIES

Stephen M. Buckley and Ritva Hurri-Syrjänen

National University of Ireland Maynooth, Department of Mathematics and Statistics
Maynooth, Co. Kildare, Ireland; stephen.buckley 'at' maths.nuim.ie

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

Abstract. We relate Orlicz-Hardy inequalities on a Euclidean domain to fatness conditions on the complement. For certain iterated log-scale distortions of Lⁿ, this relationship is necessary and sufficient, extending results of Buckley and Koskela, and others.

2010 Mathematics Subject Classification: Primary 46E35.

Key words: Hardy inequality, Orlicz spaces, capacity, uniform fatness condition.

Reference to this article: S.M. Buckley and R. Hurri-Syrjänen: Iterated log-scale Orlicz-Hardy inequalities. Ann. Acad. Sci. Fenn. Math. 38 (2013), 757-770.

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doi:10.5186/aasfm.2013.3837