| Herz空间上Littlewood-Paley g函数的加权弱有界性 |
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| 引用本文： | 孙晓华,赵凯,李加锋,郝春燕,李兰兰. Herz空间上Littlewood-Paley g函数的加权弱有界性[J]. 青岛大学学报(自然科学版), 2009, 22(4): 21-24. DOI: 10.3969/j.issn.1006-1037.2009.04.006 |
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| 作者姓名： | 孙晓华 赵凯 李加锋 郝春燕 李兰兰 |
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| 作者单位： | 青岛大学数学科学学院,山东,青岛,266071 |
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| 摘 要： | 研究了Littlewood—Paley g函数在加权Herz空间上的弱有界性。利用加权Herz空间的分解理论及几个不等式，证明了若ω1，ω2∈A1，当0〈α≤n（1-1／q）时，gφ是Kq^α,p（ω1，ω2）到WKq^α,p（ω1，ω2）上的有界算子，并且当0〈α〈n（1—1／q）时，gφ在加权Herz空间上具有强有界性。此结果丰富了Littlewood—Paley g函数的有界性理论。
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| 关 键 词： | Littlewood—Paley g函数 加权Herz空间 加权弱Herz空间 |
Weak Boundedness for Littlewood-Paley g Functions on Weighted Herz Spaces |
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| SUN Xiao-hua,ZHAO Kai,LI Jia-feng,HAO Chun-yan,LI Lan-lan. Weak Boundedness for Littlewood-Paley g Functions on Weighted Herz Spaces[J]. Journal of Qingdao University(Natural Science Edition), 2009, 22(4): 21-24. DOI: 10.3969/j.issn.1006-1037.2009.04.006 |
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| Authors: | SUN Xiao-hua ZHAO Kai LI Jia-feng HAO Chun-yan LI Lan-lan |
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| Affiliation: | (College of Mathematics, Qingdao University, Qingdao 266071, China) |
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| Abstract: | The weak boundedness on weighted Herz spaces is considered for Littlewood-Paley g functions. By the decomposition of weighted Herz space and several inequalities, it is obtained that gφ is boundedness from Kq^α,p（ω1,ω2） to WKq^α,p（ω1,ω2）, then for ω1,ω2 ∈A1, when 0〈α≤n（1- 1/q）, and gφ is strong boundedness on weighted Herz spaces when 0〈α〈n（1-1/q）. The result enriches the boundedness theory of Littlewood-Paley g functions. |
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| Keywords: | Littlewood-Paley g function weighted Herz space weighted weak Herz space |
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