Characterizations of Weighted BMO Space and Its Application

• 作者: Ding Huai WANG Jiang ZHOU Zhi Dong TENG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（8）
• 页码范围: 1278-1292
• 页数: 15页
• 语种: 英文

摘要

In this paper,we prove that the weighted BMO space BMOp(ω)=｛f ∈ L1loc:supQ||xQ||-1Lp(ω)||(f-fQ)ω-1xQ||Lp(ω)＜∞｝is independent of the scale p ∈(0,∞)in sense of norm when ω∈A1.Moreover,we can replace Lp(ω)by Lp,∞(ω).As an application,we characterize this space by the boundedness of the bilinear commutators[b,T]j(j=1,2),generated by the bilinear convolution type Calderón-Zygmund operators and the symbol b,from Lp1(ω)×LP2(ω)to Lp(ω1-p)with 1＜p1,p2＜∞ and 1/p=1/p1+1/p2.Thus we answer the open problem proposed by Chaffee affirmatively.