A note on weighted inequalities for Riemann-Liouville operators of order greater than one (Q2731408)
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scientific article; zbMATH DE number 1625982
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on weighted inequalities for Riemann-Liouville operators of order greater than one |
scientific article; zbMATH DE number 1625982 |
Statements
5 September 2002
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Riemann-Liouville fractional integrals
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two-weighted estimates in spaces of \(p\)-summable functions
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weighted inequalities
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0.92600954
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0.9228678
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0.91751033
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0.9155412
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0.9137384
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A note on weighted inequalities for Riemann-Liouville operators of order greater than one (English)
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The paper deals with two-weighted estimates for the Riemann-Liouville-type fractional operator \(R_{\alpha}\) of order \(\alpha \geq 1\) defined for \(x\in {\mathbb R}^{+}(>0)\) by NEWLINE\[NEWLINE(R_{\alpha}f)(x)=\int^{x}(x-y)^{\alpha -1}f(y) dy.NEWLINE\]NEWLINE Conditions to non-negative locally integrable functions \(u\) and \(v\) are given for the operator \(R_{\alpha}\) to be bounded from \(L_{p}({\mathbb R}^{+};v)\) into \(L_{q}({\mathbb R}^{+};u)\) with \(1<p\leq q<\infty\).
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