Real Analysis Exchange
- Real Anal. Exchange
- Volume 29, Number 2 (2003), 867-880.
An equivalence theorem for integral conditions related to Hardy's inequality.
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.
Real Anal. Exchange, Volume 29, Number 2 (2003), 867-880.
First available in Project Euclid: 7 June 2006
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 26D10: Inequalities involving derivatives and differential and integral operators 26D15: Inequalities for sums, series and integrals
Secondary: 47B07: Operators defined by compactness properties 47B38: Operators on function spaces (general)
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