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- 2016
乘积空间上的广义哈代算子的有界性
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Abstract:
摘要 研究乘积空间上的一类算子Uψf(x)=f(x1t1,…,xntn)ψ(t1,…,tn)dt1…dtn在RMO(Rn)上有界的充分必要条件,这个条件完全依赖于定义在[0,1]×…×[0,1]上的非负函数ψ。还给出了Uψ的算子范数。此外,还把这个结果推广到高维乘积空间。
[1] | <p> Carton-Lebrun C, Fosset M.Moyennes et quotinents de Taylor dans BMO[J].Bull Soc Roy Sci Liège, 1984, 53: 85-87. |
[2] | Xiao J. <em>L</em><em><sup>p</sup></em> and BMO bounds of weighted Hardy-littlewood averages[J].Math Anal Appl, 2001, 262: 660-666. |
[3] | Chen G, Wei M, Yan D.<em>L</em><em><sup>p</sup></em>-bounds of a class of mean operators on product spaces[J].Journal of University of Chinese Academy of Sciences, 2015, 32(4): 437-440. |
[4] | Campanato S.Proprieta di holderianita di alcune classi difunzioni[J].Ann Scuola Norm Sup Pisa, 1963, 17(3): 175-188. |
[5] | Zhao F, Fu Z, Lu S.Endpoint estimates for <em>n</em>-dimensional Hardy operators and their commutators[J].Science in Chaina Mathematics, 2012, 55(10): 1 977-1 990.</p> |