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 ...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, LipC(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 .展开更多
基金Supported by Xinjiang Training of Innovative Personnel Natural Science Foundation of China(2020D01C048)National Natural Science Foundation of China(11861062)。
文摘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, LipC(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 .
