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2003-2004 An equivalence theorem for integral conditions related to Hardy's inequality.
Amiram Gogatishvili, Alois Kufner, Lars-Erik Persson, Anna Wedestig
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Real Anal. Exchange 29(2): 867-880 (2003-2004).


Let $1<p\leq q<\infty .$ Inspired by some recent results concerning Hardy type inequalities we state and prove directly the equivalence of four scales of integral conditions. By applying our result to the original Hardy type inequality situation we obtain a new proof of a number of characterizations of the Hardy inequality and obtain also some new weight characterizations. As another application we prove some new weight characterizations for embeddings between some Lorentz spaces.


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Amiram Gogatishvili. Alois Kufner. Lars-Erik Persson. Anna Wedestig. "An equivalence theorem for integral conditions related to Hardy's inequality.." Real Anal. Exchange 29 (2) 867 - 880, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1070.26015
MathSciNet: MR2083821

Primary: 26D10 , 26D15
Secondary: 47B07 , 47B38

Keywords: comparisons , continuity , equivalent integral conditions , Hardy operator , Hardy's inequality , Inequalities‎ , Scales of weight characterizations , weights‎

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
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