| 齐型空间上的Lipschitz函数与Littlewood－Paley g－函数 |
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| 引用本文： | 常心怡.齐型空间上的Lipschitz函数与Littlewood－Paley g－函数[J].数学学报,1996,39(5):629-636. |
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| 作者姓名： | 常心怡 |
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| 作者单位： | 陕西师范大学数学系 |
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| 摘 要： | 在θ阶正规齐型空间上，如果算子列｛Ｓｋ｝ｋ∈Ｚ是恒等逼近，Ｄｋ＝Ｓｋ－Ｓｋ－１；本文给出一个用｛Ｄｋ｝ｋ∈Ｚ表达的ｆ∈Ｌｉｐα（Ｌｉｐｓｃｈｉｔｚ函数类，０＜α＜θ）的充分必要条件．作为其推论得到，对于ｆ∈ＬＩｐα，其Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙｇ函数ｇ（ｆ）（Ｘ）或者处处为无穷大，或者在Ｌｉｐα上有界．
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| 关 键 词： | 齐型空间，恒等逼近，Lipschitz函数，Littlewood－Paley g－函数 |
| 收稿时间： | 1994-12-26 |
| 修稿时间： | 1995-06-12 |
The Lipschitz Functions and Littlewood-Paley g-Function on Spaces of Homogeneous Type |
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| Institution: | Chang Xinyi(Department of Mathematics,Shaanxi Teacher's University, Xi'an 710062, China) |
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| Abstract: | On normal spaces of homogeneous type with orderθ,if the sequence of operators is an approximation to the identity, Dk = Sk- Sk-1, in this paper a sufficient and'necessary condition by {Dk}k∈Z for f∈Lipα(the Lipschitz function class,0<α<θ) is given.As a corollary of this result,it is obtained that the Littlewood-Paley g-function of f∈ Lip α,g(f)(x) is either infinit everywhere or bounded on Lipα. |
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| Keywords: | Space of homogeneous type Approximation to the identity Lipschitz function Littlewood-Paley g-function |
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