On the logarithmic regularity conditions for the variable exponent Hardy type inequality (Q1637849)
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scientific article; zbMATH DE number 6883060
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the logarithmic regularity conditions for the variable exponent Hardy type inequality |
scientific article; zbMATH DE number 6883060 |
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On the logarithmic regularity conditions for the variable exponent Hardy type inequality (English)
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11 June 2018
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Summary: We discuss a logarithmic regularity condition in a neighborhood of the origin and infinity on the exponent functions \(q(x) \geq p(x)\) and \(\beta(x)\) for the variable exponent Hardy inequality \( \left\|x^{\beta(\cdot)-1} \int_0^x f(t) dt \right\|_{L^{p(\cdot)}(0,l)} \leq C \left\|x^{\beta(\cdot)}f\right\|_{L^{p(\cdot)}(0,l)} \) to hold.
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Hardy-type inequality
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logarithmic regularity condition
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necessary conditions
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sufficient conditions
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0.8665385246276855
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0.8505885004997253
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0.8417832255363464
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0.8375579714775085
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