Littlewood-Paley g-函数与加权BMO函数

Littlewood-Paley g-Functions and Weighted BMO

设gφ,b是Littlewood-Paley g-函数与b生成的交换子.本文证明了若α,β属于Muckenhoupt A_p权函数类,1<P<∞,b∈BMO(v),v=(αβ^(-1))1/p,那么交换子gφ,b是L^P(α)到L^P(β)的有界算子.

Let 9ψ,b denote the commutator generated by g-function and b. In this paper, we show that if α and β belong to class of Ap weights, 1 〈 p 〈 ∞, b ∈ BMO（v） and v = （αβ-1） 1/p, then gψ,b is a bounded operator from LP（α） into LP（β）.