Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces
Let (X,d,μ) be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hytönen. The aim of this paper is to establish the boundedness of commutator Mb generated by the Marcinkiewicz integral M and Lipschitz function b. The authors prove tha...
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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/10.1155/2015/548165 |
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| author | Guanghui Lu Shuangping Tao |
| author_facet | Guanghui Lu Shuangping Tao |
| author_sort | Guanghui Lu |
| collection | DOAJ |
| description | Let (X,d,μ) be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hytönen. The aim of this paper is to establish the boundedness of commutator Mb generated by the Marcinkiewicz integral M and Lipschitz function b. The authors prove that Mb is bounded from the Lebesgue spaces Lp(μ) to weak Lebesgue spaces Lq(μ) for 1≤p<n/β, from the Lebesgue spaces Lp(μ) to the spaces RBMO(μ) for p=n/β, and from the Lebesgue spaces Lp(μ) to the Lipschitz spaces Lip(β-n/p)(μ) for n/β<p≤∞. Moreover, some results in Morrey spaces and Hardy spaces are also discussed. |
| format | Article |
| id | doaj-art-42db7549e08840909aa8013080bc54f4 |
| 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-42db7549e08840909aa8013080bc54f42025-02-03T06:00:57ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/548165548165Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure SpacesGuanghui Lu0Shuangping Tao1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaLet (X,d,μ) be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hytönen. The aim of this paper is to establish the boundedness of commutator Mb generated by the Marcinkiewicz integral M and Lipschitz function b. The authors prove that Mb is bounded from the Lebesgue spaces Lp(μ) to weak Lebesgue spaces Lq(μ) for 1≤p<n/β, from the Lebesgue spaces Lp(μ) to the spaces RBMO(μ) for p=n/β, and from the Lebesgue spaces Lp(μ) to the Lipschitz spaces Lip(β-n/p)(μ) for n/β<p≤∞. Moreover, some results in Morrey spaces and Hardy spaces are also discussed.http://dx.doi.org/10.1155/2015/548165 |
| spellingShingle | Guanghui Lu Shuangping Tao Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces Journal of Function Spaces |
| title | Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces |
| title_full | Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces |
| title_fullStr | Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces |
| title_full_unstemmed | Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces |
| title_short | Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces |
| title_sort | boundedness of commutators of marcinkiewicz integrals on nonhomogeneous metric measure spaces |
| url | http://dx.doi.org/10.1155/2015/548165 |
| work_keys_str_mv | AT guanghuilu boundednessofcommutatorsofmarcinkiewiczintegralsonnonhomogeneousmetricmeasurespaces AT shuangpingtao boundednessofcommutatorsofmarcinkiewiczintegralsonnonhomogeneousmetricmeasurespaces |