Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces
Let (X,d,μ) be a metric measure space which satisfies the geometrically doubling measure and the upper doubling measure conditions. In this paper, the authors prove that, under the assumption that the kernel of Mκ⁎ satisfies a certain Hörmander-type condition, Mκ⁎,ρ is bounded from Lebesgue spaces L...
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/9091478 |
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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 which satisfies the geometrically doubling measure and the upper doubling measure conditions. In this paper, the authors prove that, under the assumption that the kernel of Mκ⁎ satisfies a certain Hörmander-type condition, Mκ⁎,ρ is bounded from Lebesgue spaces Lp(μ) to Lebesgue spaces Lp(μ) for p≥2 and is bounded from L1(μ) into L1,∞(μ). As a corollary, Mκ⁎,ρ is bounded on Lp(μ) for 1<p<2. In addition, the authors also obtain that Mκ⁎,ρ is bounded from the atomic Hardy space H1(μ) into the Lebesgue space L1(μ). |
| format | Article |
| id | doaj-art-a0ac28608e824ed9a6772a68aa2968d4 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a0ac28608e824ed9a6772a68aa2968d42025-02-03T05:59:05ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/90914789091478Estimates for Parameter Littlewood-Paley gκ⁎ Functions 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 which satisfies the geometrically doubling measure and the upper doubling measure conditions. In this paper, the authors prove that, under the assumption that the kernel of Mκ⁎ satisfies a certain Hörmander-type condition, Mκ⁎,ρ is bounded from Lebesgue spaces Lp(μ) to Lebesgue spaces Lp(μ) for p≥2 and is bounded from L1(μ) into L1,∞(μ). As a corollary, Mκ⁎,ρ is bounded on Lp(μ) for 1<p<2. In addition, the authors also obtain that Mκ⁎,ρ is bounded from the atomic Hardy space H1(μ) into the Lebesgue space L1(μ).http://dx.doi.org/10.1155/2016/9091478 |
| spellingShingle | Guanghui Lu Shuangping Tao Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces Journal of Function Spaces |
| title | Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces |
| title_full | Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces |
| title_fullStr | Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces |
| title_full_unstemmed | Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces |
| title_short | Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces |
| title_sort | estimates for parameter littlewood paley gκ functions on nonhomogeneous metric measure spaces |
| url | http://dx.doi.org/10.1155/2016/9091478 |
| work_keys_str_mv | AT guanghuilu estimatesforparameterlittlewoodpaleygkfunctionsonnonhomogeneousmetricmeasurespaces AT shuangpingtao estimatesforparameterlittlewoodpaleygkfunctionsonnonhomogeneousmetricmeasurespaces |