摘要
设μ,λ∈Ap,V=(μλ-1)1/p,1<p<∞,b∈L1(dx),如果b∈BMOV,则换位子[T,Mb]满足:存在一个常数Cf与f有关,使得∫|[T,Mb]f-Cf|pλ≤C∫|f|pμ;相反地若Ci=[Ri,Mb]是Lp(Rn,μ)到Lp(Rn,λ)有界算子,即∫Rn|[Ri,Mb]f|pλ≤C∫Rn|f|pμ,(i=1,2,…,n),则b∈BMOv.此结果推广了Bloom(1985)所得到的结果.
Suppose u,λ∈A p and V=(μλ -1 ) 1/p , b∈L 1(dx), where 1<p<∞; if b∈BMO V, the commutator satisfies:existence of a constant C f such that ∫|[T,M b]f-C f| pλ≤c∫|f| pu. Conversely, if C i=[R i,M b] is a boumded operator from L p(R n,u) to L p(R n,λ),∫ R n |[R i,M b]f| pλ≤C∫ R n |f| pμ(i=1,2,…,n), then b∈BMO V.