Weighted inequalities for the Riemann--Liouville operators on piecewise monotone functions (Q2773584)
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scientific article; zbMATH DE number 1710218
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weighted inequalities for the Riemann--Liouville operators on piecewise monotone functions |
scientific article; zbMATH DE number 1710218 |
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24 February 2002
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integral operator
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Riemann-Liouville operator
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weighted inequalities
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Weighted inequalities for the Riemann--Liouville operators on piecewise monotone functions (English)
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The author exposes necessary and sufficient conditions for boundedness of integral operators of the form NEWLINE\[NEWLINE I_{\alpha}f(x) = \int_0^x(x-y)^{\alpha - 1}f(y) dy,\quad J_{\alpha}g(x) = \int_x^{\infty}(y-x)^{\alpha - 1}g(y) dy NEWLINE\]NEWLINE which act from \(L_{p,w}[0,\infty)\) to \(L_{q,v}[0,\infty)\), where \(\alpha > 0\), \(1 < p,q<\infty\) and \(f(y)\), \(g(y)\) are piecewise monotone functions.
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