Generalized Fractional Integral Operators on Generalized Local Morrey Spaces
We study the continuity properties of the generalized fractional integral operator Iρ on the generalized local Morrey spaces LMp,φ{x0} and generalized Morrey spaces Mp,φ. We find conditions on the triple (φ1,φ2,ρ) which ensure the Spanne-type boundedness of Iρ from one generalized local Morrey space...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/594323 |
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| author | V. S. Guliyev A. F. Ismayilova A. Kucukaslan A. Serbetci |
| author_facet | V. S. Guliyev A. F. Ismayilova A. Kucukaslan A. Serbetci |
| author_sort | V. S. Guliyev |
| collection | DOAJ |
| description | We study the continuity properties of the generalized fractional integral operator Iρ on the generalized local Morrey spaces LMp,φ{x0} and generalized Morrey spaces Mp,φ. We find conditions on the triple (φ1,φ2,ρ) which ensure the Spanne-type boundedness of Iρ from one generalized local Morrey space LMp,φ1{x0} to another LMq,φ2{x0}, 1<p<q<∞, and from LM1,φ1{x0} to the weak space WLMq,φ2{x0}, 1<q<∞. We also find conditions on the pair (φ,ρ) which ensure the Adams-type boundedness of Iρ from Mp,φ1/p to Mq,φ1/q for 1<p<q<∞ and from M1,φ to WMq,φ1/q for 1<q<∞. In all cases the conditions for the boundedness of Iρ are given in terms of Zygmund-type integral inequalities on (φ1,φ2,ρ) and (φ,ρ), which do not assume any assumption on monotonicity of φ1(x,r), φ2(x,r), and φ(x,r) in r. |
| format | Article |
| id | doaj-art-05b8bfa1f9a7461f83d60486dc3639f0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-05b8bfa1f9a7461f83d60486dc3639f02025-02-03T01:22:12ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/594323594323Generalized Fractional Integral Operators on Generalized Local Morrey SpacesV. S. Guliyev0A. F. Ismayilova1A. Kucukaslan2A. Serbetci3Department of Mathematics, Ahi Evran University, Bagbasi Campus, 40100 Kirsehir, TurkeyInstitute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, B. Vahabzade Street 9, 1141 Baku, AzerbaijanDepartment of Mathematics, Ankara University, Tandogan, 06100 Ankara, TurkeyDepartment of Mathematics, Ankara University, Tandogan, 06100 Ankara, TurkeyWe study the continuity properties of the generalized fractional integral operator Iρ on the generalized local Morrey spaces LMp,φ{x0} and generalized Morrey spaces Mp,φ. We find conditions on the triple (φ1,φ2,ρ) which ensure the Spanne-type boundedness of Iρ from one generalized local Morrey space LMp,φ1{x0} to another LMq,φ2{x0}, 1<p<q<∞, and from LM1,φ1{x0} to the weak space WLMq,φ2{x0}, 1<q<∞. We also find conditions on the pair (φ,ρ) which ensure the Adams-type boundedness of Iρ from Mp,φ1/p to Mq,φ1/q for 1<p<q<∞ and from M1,φ to WMq,φ1/q for 1<q<∞. In all cases the conditions for the boundedness of Iρ are given in terms of Zygmund-type integral inequalities on (φ1,φ2,ρ) and (φ,ρ), which do not assume any assumption on monotonicity of φ1(x,r), φ2(x,r), and φ(x,r) in r.http://dx.doi.org/10.1155/2015/594323 |
| spellingShingle | V. S. Guliyev A. F. Ismayilova A. Kucukaslan A. Serbetci Generalized Fractional Integral Operators on Generalized Local Morrey Spaces Journal of Function Spaces |
| title | Generalized Fractional Integral Operators on Generalized Local Morrey Spaces |
| title_full | Generalized Fractional Integral Operators on Generalized Local Morrey Spaces |
| title_fullStr | Generalized Fractional Integral Operators on Generalized Local Morrey Spaces |
| title_full_unstemmed | Generalized Fractional Integral Operators on Generalized Local Morrey Spaces |
| title_short | Generalized Fractional Integral Operators on Generalized Local Morrey Spaces |
| title_sort | generalized fractional integral operators on generalized local morrey spaces |
| url | http://dx.doi.org/10.1155/2015/594323 |
| work_keys_str_mv | AT vsguliyev generalizedfractionalintegraloperatorsongeneralizedlocalmorreyspaces AT afismayilova generalizedfractionalintegraloperatorsongeneralizedlocalmorreyspaces AT akucukaslan generalizedfractionalintegraloperatorsongeneralizedlocalmorreyspaces AT aserbetci generalizedfractionalintegraloperatorsongeneralizedlocalmorreyspaces |