齐型空间上Little wood-Paley“非汉字符号”-函数的Lipα有界性  

LipαBoundedness of Littlewood-Paley “非汉字符号” Function on Spaces of Homogeneous Type

作　　者：李富民[1] 

机构地区：[1]西安石油学院信息科学系,陕西西安710065

出　　处：《西安石油学院学报（自然科学版）》2001年第4期85-88,共4页Journal of Xi'an Petroleum Institute（Natural Science Edition)

摘　　要：在θ阶正规齐型空间上 ,设算子列 {Sk}k∈ Z是恒等逼近 ,记 Dk =Sk- Sk-1,DNk =∑| j| <NDk+ j( N充分大 ) ,TN=∑k∈ zDNk Dk,Dk=T-1N DNk,给出了用 {Dk}k∈ z表达的 f∈ Lipα( 0 <α<min{θ,ε,ε′})的必要条件 ,得到了对于 f∈ Lipα,其 Littlewood- Paley g-函数 g( f ) ( x) ,若在一点有限则在 Lipα上有界 .On normal spaces of homogeneous type x with θ order, suppose the sequence of operators {S k} k∈z  is identically approaching, that is, D k=S k-S k-1 ,D N k=∑|J|<ND k+j ,T N=∑k∈zD N kD k, k=T -1 ND k . A necessary condition of f∈Lipα(0<α≤min{θ,ε,ε′}) was given by  {D k} k∈z . And it is obtainted that, if (f)(x),the Littlewood-Paley  function of f∈Lipα,has finite value at a single point in x, it is bounded on Lipα.

关 键 词：齐型空间 LIPSCHITZ函数 LITTLEWOOD-PALEY g^^-函数 恒等逼近 有界性 Lipα 

分 类 号：O174.3[理学—数学]