齐型空间上Lipschitz函数的一个新刻画  

A New Characteristic of Lipschitz Function in Homogeneous Space

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）》2002年第5期80-82,85,共4页Journal of Xi'an Petroleum Institute（Natural Science Edition)

摘　　要：Suppose ( X,ρ,μ ) is a normal homogeneous space with order θ , the sequence of operators { S k} k∈z is an identical approximation, and set D k=S k-S k-1 . A new characteristic of the function f∈Lip α (Lipschitz function spaces {S k} k∈z , 0< α <min{ σ,ε } is given by {D k} k∈z : suppose function f is integrable on every boundet set, LipC(M(β,r))′ in the equivalent sense, then a necessary and sufficient condition for f∈Lipα is given by k∈z |D k(f)(x)-D k(f)(y)| 2] 1/2 ≤Cρ(x,y) α,x,y∈z, where constant C does not depend on x ,y and f . 1/2 ≤Cρ(x,y) α,x,y∈z, where constant C does not depend on x ,y and f .Suppose ( X,ρ,μ ) is a normal homogeneous space with order θ , the sequence of operators { S k} k∈z is an identical approximation, and set D k=S k-S k-1 . A new characteristic of the function f∈Lip α (Lipschitz function spaces {S k} k∈z , 0< α <min{ σ,ε } is given by {D k} k∈z : suppose function f is integrable on every boundet set, LipC(M(β,r))′ in the equivalent sense, then a necessary and sufficient condition for f∈Lipα is given by k∈z |D k(f)(x)-D k(f)(y)| 2] 1/2 ≤Cρ(x,y) α,x,y∈z, where constant C does not depend on x ,y and f . 1/2 ≤Cρ(x,y) α,x,y∈z, where constant C does not depend on x ,y and f .

关 键 词：齐型空间 LIPSCHITZ函数 恒等逼近 

分 类 号：O174.41[理学—数学]