Carleman-Knopp type inequalities via Hardy inequalities (Q2745652)
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scientific article; zbMATH DE number 1654983
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Carleman-Knopp type inequalities via Hardy inequalities |
scientific article; zbMATH DE number 1654983 |
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Carleman-Knopp type inequalities via Hardy inequalities (English)
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14 July 2002
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Hardy inequality
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Carleman inequality
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Knopp inequality
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0.93634355
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0.9357008
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0.92550063
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0.9182509
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This paper outlines an important technique to prove inequalities of the form NEWLINE\[NEWLINE\Biggl(\int^b_0 \Biggl[\exp\Biggl({1\over x} \int^x_0\ln f(t) dt\Biggr)\Biggr]^q w(x) dx\Biggr)^{1/q}\leq C\Biggl(\int^b_0 f^p(x)v(x) dx\Biggr)^{1/p}NEWLINE\]NEWLINE (for \(0< b\leq\infty\) and \(0< q< p<\infty\)) as ``end point'' inequalities of the weighted Hardy inequality. Moreover, some reversed Carleman-Knopp inequalities are derived and applied.
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