Generalized Stepanov spaces and the fractional Liouville integral (Q2723275)
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scientific article; zbMATH DE number 1614383
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized Stepanov spaces and the fractional Liouville integral |
scientific article; zbMATH DE number 1614383 |
Statements
5 July 2001
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Liouville operator
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generalized Stepanov space
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Generalized Stepanov spaces and the fractional Liouville integral (English)
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The authors give a sufficient condition on a function \(\varphi\) under which the Liouville operator NEWLINE\[NEWLINE(I^\alpha f)(t)= {1\over\Gamma(\alpha)} \int^t_0 (t-s)^{\alpha- 1}f(s) ds\qquad (0\leq t<\infty)NEWLINE\]NEWLINE is bounded in the corresponding generalized Stepanov space \(S_{p,\varphi}\) introduced by the second author [Mat. Zametki 6, No. 4, 463-473 (1969; Zbl 0194.43703)].
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0.7828167676925659
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0.7735773324966431
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