Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces
We prove that b is in Lipβ(ω) if and only if the commutator [b,L-α/2] of the multiplication operator by b and the general fractional integral operator L-α/2 is bounded from the weighted Morrey space Lp,k(ω) to Lq,kq/p(ω1-(1-α/n)q,ω), where 0<β<1, 0<α+β<n,1<p<n/(α+β), 1/q=1/p-(α+β)/...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/929381 |
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| author | Zengyan Si Fayou Zhao |
| author_facet | Zengyan Si Fayou Zhao |
| author_sort | Zengyan Si |
| collection | DOAJ |
| description | We prove that b is in Lipβ(ω) if and only if the commutator [b,L-α/2] of the multiplication operator by b and the general fractional integral operator L-α/2 is bounded from the weighted Morrey space Lp,k(ω) to Lq,kq/p(ω1-(1-α/n)q,ω), where 0<β<1, 0<α+β<n,1<p<n/(α+β), 1/q=1/p-(α+β)/n, 0≤k<p/q, ωq/p∈A1, and rω>(1-k)/(p/(q-k)), and here rω denotes the critical index of ω for the reverse Hölder condition. |
| format | Article |
| id | doaj-art-005c9130be5742b182b606c323cf6767 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-005c9130be5742b182b606c323cf67672025-02-03T07:24:50ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/929381929381Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey SpacesZengyan Si0Fayou Zhao1School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaWe prove that b is in Lipβ(ω) if and only if the commutator [b,L-α/2] of the multiplication operator by b and the general fractional integral operator L-α/2 is bounded from the weighted Morrey space Lp,k(ω) to Lq,kq/p(ω1-(1-α/n)q,ω), where 0<β<1, 0<α+β<n,1<p<n/(α+β), 1/q=1/p-(α+β)/n, 0≤k<p/q, ωq/p∈A1, and rω>(1-k)/(p/(q-k)), and here rω denotes the critical index of ω for the reverse Hölder condition.http://dx.doi.org/10.1155/2012/929381 |
| spellingShingle | Zengyan Si Fayou Zhao Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces Abstract and Applied Analysis |
| title | Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces |
| title_full | Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces |
| title_fullStr | Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces |
| title_full_unstemmed | Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces |
| title_short | Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces |
| title_sort | necessary and sufficient conditions for boundedness of commutators of the general fractional integral operators on weighted morrey spaces |
| url | http://dx.doi.org/10.1155/2012/929381 |
| work_keys_str_mv | AT zengyansi necessaryandsufficientconditionsforboundednessofcommutatorsofthegeneralfractionalintegraloperatorsonweightedmorreyspaces AT fayouzhao necessaryandsufficientconditionsforboundednessofcommutatorsofthegeneralfractionalintegraloperatorsonweightedmorreyspaces |