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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/4876146 |
| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |