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## Banach Center Publications

2004 | 64 | 1 | 135-146
Tytuł artykułu

### A study of some constants characterizing the weighted Hardy inequality

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EN
The modern form of Hardy's inequality means that we have a necessary and sufficient condition on the weights u and v on [0,b] so that the mapping <br> $H: L^{p}(0,b;v) → L^{q}(0,b;u)$ <br> is continuous, where $Hf(x) = ∫_{0}^{x} f(t)dt$ is the Hardy operator. We consider the case 1 < p ≤ q < ∞ and then this condition is usually written in the Muckenhoupt form <br> (*) $A₁: = sup_{0<x<b}A_{M}(x) < ∞$. <br> In this paper we discuss and compare some old and new other constants $A_{i}$ of the form (*), which also characterize Hardy's inequality. We also point out some dual forms of these characterizations, prove some new compactness results and state some open problems.
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Tom
Numer
Strony
135-146
Opis fizyczny
Daty
wydano
2004
Twórcy
autor
• Matematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
autor
• Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
autor
• Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
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