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.
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.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
1996年第5期629-636,共8页
Acta Mathematica Sinica:Chinese Series
关键词
齐型空间
LIPSCHITZ函数
L-P函数
G-函数
Space of homogeneous type
Approximation to the identity
Lipschitz function
Littlewood-Paley g-function