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
This manuscript addresses Muckenhoupt A_p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A_p class,if and only if Hardy-Littlewood maximal function M is bounded from ...This manuscript addresses Muckenhoupt A_p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A_p class,if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces L^p(ω) to weighted Morrey spaces M_q^p(ω) for 1<q<p<∞. As a corollary,if M is(weak) bounded on M_q^p(ω),then ω∈A_p. The A_p condition also characterizes the boundedness of the Riesz transform R_j and convolution operators T_e on weighted Morrey spaces. Finally,we show that ω∈A_p if and only if ω∈ BMO^(p′)(ω) for 1≤p<∞ and 1/p+1/p′= 1.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.
基金supported by National Natural Science Foundation of China(Grant No.11661075)
文摘This manuscript addresses Muckenhoupt A_p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A_p class,if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces L^p(ω) to weighted Morrey spaces M_q^p(ω) for 1<q<p<∞. As a corollary,if M is(weak) bounded on M_q^p(ω),then ω∈A_p. The A_p condition also characterizes the boundedness of the Riesz transform R_j and convolution operators T_e on weighted Morrey spaces. Finally,we show that ω∈A_p if and only if ω∈ BMO^(p′)(ω) for 1≤p<∞ and 1/p+1/p′= 1.
