Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces
Let L be the infinitesimal generator of an analytic semigroup on L2(Rn) with Gaussian kernel bounds, and let L-α/2 be the fractional integrals of L for 0<α<n. For any locally integrable function b, the commutators associated with L-α/2 are defined by [b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/413716 |
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| _version_ | 1832566207993085952 |
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| author | Zhiheng Wang Zengyan Si |
| author_facet | Zhiheng Wang Zengyan Si |
| author_sort | Zhiheng Wang |
| collection | DOAJ |
| description | Let L be the infinitesimal generator of an analytic semigroup on L2(Rn) with Gaussian kernel bounds, and let L-α/2 be the fractional integrals of L for 0<α<n. For any locally integrable function b, the commutators associated with L-α/2 are defined by [b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x). When b∈BMO(ω) (weighted BMO space) or b∈BMO, the authors obtain the necessary and sufficient conditions for the boundedness of [b,L-α/2] on weighted Morrey spaces, respectively. |
| format | Article |
| id | doaj-art-5cb5616160434c76b4a444cc32a2defd |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5cb5616160434c76b4a444cc32a2defd2025-02-03T01:04:42ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/413716413716Commutator Theorems for Fractional Integral Operators on Weighted Morrey SpacesZhiheng Wang0Zengyan Si1School of Computer Science and Technique, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, ChinaLet L be the infinitesimal generator of an analytic semigroup on L2(Rn) with Gaussian kernel bounds, and let L-α/2 be the fractional integrals of L for 0<α<n. For any locally integrable function b, the commutators associated with L-α/2 are defined by [b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x). When b∈BMO(ω) (weighted BMO space) or b∈BMO, the authors obtain the necessary and sufficient conditions for the boundedness of [b,L-α/2] on weighted Morrey spaces, respectively.http://dx.doi.org/10.1155/2014/413716 |
| spellingShingle | Zhiheng Wang Zengyan Si Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces Abstract and Applied Analysis |
| title | Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces |
| title_full | Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces |
| title_fullStr | Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces |
| title_full_unstemmed | Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces |
| title_short | Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces |
| title_sort | commutator theorems for fractional integral operators on weighted morrey spaces |
| url | http://dx.doi.org/10.1155/2014/413716 |
| work_keys_str_mv | AT zhihengwang commutatortheoremsforfractionalintegraloperatorsonweightedmorreyspaces AT zengyansi commutatortheoremsforfractionalintegraloperatorsonweightedmorreyspaces |