## Real Analysis Exchange

### An equivalence theorem for integral conditions related to Hardy's inequality.

#### Abstract

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.

#### Article information

Source
Real Anal. Exchange, Volume 29, Number 2 (2003), 867-880.

Dates
First available in Project Euclid: 7 June 2006

https://projecteuclid.org/euclid.rae/1149698549

Mathematical Reviews number (MathSciNet)
MR2083821

Zentralblatt MATH identifier
1070.26015

#### Citation

Gogatishvili, Amiram; Kufner, Alois; Persson, Lars-Erik; Wedestig, Anna. An equivalence theorem for integral conditions related to Hardy's inequality. Real Anal. Exchange 29 (2003), no. 2, 867--880. https://projecteuclid.org/euclid.rae/1149698549

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