In this paper,we prove that the weighted BMO space BMO^(p)(ω)={f∈L^(1)_(loc):sup||χQ||^(-1)Lp(ω)||(F-Fq)ω^(-1)χQ||LP(ω)<∞Q}is independent of the scale p∈(0,∞)in sense of norm whenω∈A_(1).Moreover,we can...In this paper,we prove that the weighted BMO space BMO^(p)(ω)={f∈L^(1)_(loc):sup||χQ||^(-1)Lp(ω)||(F-Fq)ω^(-1)χQ||LP(ω)<∞Q}is independent of the scale p∈(0,∞)in sense of norm whenω∈A_(1).Moreover,we can replace L^(p)(ω)by L^(p,∞)(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 Calderdn-Zygmund operators and the symbol b,from L^(p1)(ω)×L^(p2)(ω)to L^(p)(ω^(1-p))with 1<p1,p2<∞and 1/p=1/p1+1/p2.Thus we answer the open problem proposed by Chaffee affirmatively.展开更多
基金Supported by National Natural Science Foundation of China(Nos.11971237,12071223)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.19KJA320001)Doctoral Scientific Research Foundation(Grant No.903/752041)。
文摘In this paper,we prove that the weighted BMO space BMO^(p)(ω)={f∈L^(1)_(loc):sup||χQ||^(-1)Lp(ω)||(F-Fq)ω^(-1)χQ||LP(ω)<∞Q}is independent of the scale p∈(0,∞)in sense of norm whenω∈A_(1).Moreover,we can replace L^(p)(ω)by L^(p,∞)(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 Calderdn-Zygmund operators and the symbol b,from L^(p1)(ω)×L^(p2)(ω)to L^(p)(ω^(1-p))with 1<p1,p2<∞and 1/p=1/p1+1/p2.Thus we answer the open problem proposed by Chaffee affirmatively.
