Estimates for Multilinear Commutators of Generalized 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. Assume that b→=(b1,b2,…,bm) is a finite family of locally integrable functions; then the multilinear commutators generated by b→ and L-...
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/670649 |
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| author | Sha He Taotao Zheng Xiangxing Tao |
| author_facet | Sha He Taotao Zheng Xiangxing Tao |
| author_sort | Sha He |
| 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. Assume that b→=(b1,b2,…,bm) is a finite family of locally integrable functions; then the multilinear commutators generated by b→ and L-α/2 are defined by Lb→-α/2f=[bm,…,[b2,[b1,L-α/2]],…]f. Assume that bj belongs to weighted BMO space, j=1,2,…,m; the authors obtain the boundedness of Lb→-α/2 on weighted Morrey spaces. As a special case, when L=-Δ is the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutator Iαb→ on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results. |
| format | Article |
| id | doaj-art-89d55ccd29784b4da98e6621f1c51dd5 |
| 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-89d55ccd29784b4da98e6621f1c51dd52025-02-03T05:59:52ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/670649670649Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey SpacesSha He0Taotao Zheng1Xiangxing Tao2School of Mathematical Sciences, Beijing Normal University, and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaDepartment of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, ChinaDepartment of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, 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. Assume that b→=(b1,b2,…,bm) is a finite family of locally integrable functions; then the multilinear commutators generated by b→ and L-α/2 are defined by Lb→-α/2f=[bm,…,[b2,[b1,L-α/2]],…]f. Assume that bj belongs to weighted BMO space, j=1,2,…,m; the authors obtain the boundedness of Lb→-α/2 on weighted Morrey spaces. As a special case, when L=-Δ is the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutator Iαb→ on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results.http://dx.doi.org/10.1155/2015/670649 |
| spellingShingle | Sha He Taotao Zheng Xiangxing Tao Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces Journal of Function Spaces |
| title | Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces |
| title_full | Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces |
| title_fullStr | Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces |
| title_full_unstemmed | Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces |
| title_short | Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces |
| title_sort | estimates for multilinear commutators of generalized fractional integral operators on weighted morrey spaces |
| url | http://dx.doi.org/10.1155/2015/670649 |
| work_keys_str_mv | AT shahe estimatesformultilinearcommutatorsofgeneralizedfractionalintegraloperatorsonweightedmorreyspaces AT taotaozheng estimatesformultilinearcommutatorsofgeneralizedfractionalintegraloperatorsonweightedmorreyspaces AT xiangxingtao estimatesformultilinearcommutatorsofgeneralizedfractionalintegraloperatorsonweightedmorreyspaces |