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A note on a two-weighted Sobolev inequality

100%

Gurka P., Kufner A.

Banach Center Publications

1989

tom 22

nr 1

169-172

A study of some constants characterizing the weighted Hardy inequality

81%

Kufner A., Persson L.-E., Wedestig A.

Banach Center Publications

2004

tom 64

nr 1

135-146

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
$H: L^{p}(0,b;v) → L^{q}(0,b;u)$
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
(*) $A₁: = sup_{0 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.

Ograniczanie wyników

2 Banach Center Publications

2 Kufner A.

1 Gurka P.

1 Persson L.-E.

1 Wedestig A.

1 2004

1 1989

Wyniki wyszukiwania

A note on a two-weighted Sobolev inequality

A study of some constants characterizing the weighted Hardy inequality