A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space
The variable exponent Hardy inequality xβ(x)-1∫0xf(t)dtLp(.)(0,l)≤Cxβ(x)fLp(.)(0,l), f≥0 is proved assuming that the exponents p:(0,l)→(1,∞), β:(0,l)→ℝ not rapidly oscilate near origin and 1/p′(0)-β>0. The main result is a necessary and sufficient condition on p, β generalizing known results on...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/342910 |
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