Multilinear Square Functions with Kernels of Dini’s Type
Let T be a multilinear square function with a kernel satisfying Dini(1) condition and let T⁎ be the corresponding multilinear maximal square function. In this paper, first, we showed that T is bounded from L1×⋯×L1 to L1/m,∞. Secondly, we obtained that if each pi>1, then T and T⁎ are bounded from...
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| Format: | Article |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/4876146 |
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| author | Zengyan Si Qingying Xue |
| author_facet | Zengyan Si Qingying Xue |
| author_sort | Zengyan Si |
| collection | DOAJ |
| description | Let T be a multilinear square function with a kernel satisfying Dini(1) condition and let T⁎ be the corresponding multilinear maximal square function. In this paper, first, we showed that T is bounded from L1×⋯×L1 to L1/m,∞. Secondly, we obtained that if each pi>1, then T and T⁎ are bounded from Lp1(ω1)×⋯×Lpm(ωm) to Lp(νω→) and if there is pi=1, then T and T⁎ are bounded from Lp1(ω1)×⋯×Lpm(ωm) to Lp,∞(νω→), where νω→=∏i=1mωip/pi. Furthermore, we established the weighted strong and weak type boundedness for T and T⁎ on weighted Morrey type spaces, respectively. |
| format | Article |
| id | doaj-art-c1e91c9b142d44f38fe86739e4928427 |
| 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-c1e91c9b142d44f38fe86739e49284272025-02-03T01:02:50ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/48761464876146Multilinear Square Functions with Kernels of Dini’s TypeZengyan Si0Qingying Xue1School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, ChinaSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaLet T be a multilinear square function with a kernel satisfying Dini(1) condition and let T⁎ be the corresponding multilinear maximal square function. In this paper, first, we showed that T is bounded from L1×⋯×L1 to L1/m,∞. Secondly, we obtained that if each pi>1, then T and T⁎ are bounded from Lp1(ω1)×⋯×Lpm(ωm) to Lp(νω→) and if there is pi=1, then T and T⁎ are bounded from Lp1(ω1)×⋯×Lpm(ωm) to Lp,∞(νω→), where νω→=∏i=1mωip/pi. Furthermore, we established the weighted strong and weak type boundedness for T and T⁎ on weighted Morrey type spaces, respectively.http://dx.doi.org/10.1155/2016/4876146 |
| spellingShingle | Zengyan Si Qingying Xue Multilinear Square Functions with Kernels of Dini’s Type Journal of Function Spaces |
| title | Multilinear Square Functions with Kernels of Dini’s Type |
| title_full | Multilinear Square Functions with Kernels of Dini’s Type |
| title_fullStr | Multilinear Square Functions with Kernels of Dini’s Type |
| title_full_unstemmed | Multilinear Square Functions with Kernels of Dini’s Type |
| title_short | Multilinear Square Functions with Kernels of Dini’s Type |
| title_sort | multilinear square functions with kernels of dini s type |
| url | http://dx.doi.org/10.1155/2016/4876146 |
| work_keys_str_mv | AT zengyansi multilinearsquarefunctionswithkernelsofdinistype AT qingyingxue multilinearsquarefunctionswithkernelsofdinistype |