Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces
We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev ine...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/809704 |
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| _version_ | 1832566711744724992 |
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| author | Hendra Gunawan Denny Ivanal Hakim Yoshihiro Sawano Idha Sihwaningrum |
| author_facet | Hendra Gunawan Denny Ivanal Hakim Yoshihiro Sawano Idha Sihwaningrum |
| author_sort | Hendra Gunawan |
| collection | DOAJ |
| description | We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces. |
| format | Article |
| id | doaj-art-cca929cb83d74222ba11cd0880d00fb7 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-cca929cb83d74222ba11cd0880d00fb72025-02-03T01:03:31ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/809704809704Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey SpacesHendra Gunawan0Denny Ivanal Hakim1Yoshihiro Sawano2Idha Sihwaningrum3Department of Mathematics, Bandung Institute of Technology, Bandung 41032, IndonesiaDepartment of Mathematics, Bandung Institute of Technology, Bandung 41032, IndonesiaDepartment of Mathematics and Information Sciences, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, JapanDepartment of Mathematics, Jenderal Soedirman University, Purwokerto 53122, IndonesiaWe prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces.http://dx.doi.org/10.1155/2013/809704 |
| spellingShingle | Hendra Gunawan Denny Ivanal Hakim Yoshihiro Sawano Idha Sihwaningrum Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces Journal of Function Spaces and Applications |
| title | Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces |
| title_full | Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces |
| title_fullStr | Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces |
| title_full_unstemmed | Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces |
| title_short | Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces |
| title_sort | weak type inequalities for some integral operators on generalized nonhomogeneous morrey spaces |
| url | http://dx.doi.org/10.1155/2013/809704 |
| work_keys_str_mv | AT hendragunawan weaktypeinequalitiesforsomeintegraloperatorsongeneralizednonhomogeneousmorreyspaces AT dennyivanalhakim weaktypeinequalitiesforsomeintegraloperatorsongeneralizednonhomogeneousmorreyspaces AT yoshihirosawano weaktypeinequalitiesforsomeintegraloperatorsongeneralizednonhomogeneousmorreyspaces AT idhasihwaningrum weaktypeinequalitiesforsomeintegraloperatorsongeneralizednonhomogeneousmorreyspaces |