On the Riesz Potential and Its Commutators on Generalized Orlicz-Morrey Spaces
We consider generalized Orlicz-Morrey spaces MΦ,φ(ℝn) including their weak versions WMΦ,φ(ℝn). In these spaces we prove the boundedness of the Riesz potential from MΦ,φ1(ℝn) to MΨ,φ2(ℝn) and from MΦ,φ1(ℝn) to WMΨ,φ2(ℝn). As applications of those results, the boundedness of the commutators of the Rie...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/617414 |
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| Summary: | We consider generalized Orlicz-Morrey spaces MΦ,φ(ℝn) including their weak versions WMΦ,φ(ℝn). In these spaces we prove the boundedness of the Riesz potential from MΦ,φ1(ℝn) to MΨ,φ2(ℝn) and from MΦ,φ1(ℝn) to WMΨ,φ2(ℝn). As applications of those results, the boundedness of the commutators of the Riesz potential on generalized Orlicz-Morrey space is also obtained. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on (φ1,φ2), which do not assume any assumption on monotonicity of φ1(x,r), φ2(x,r) in r. |
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| ISSN: | 2314-8896 2314-8888 |