粗糙核极大算子交换子的加权有界性

对粗糙核分数次极大算子与BMO函数生成的m阶(m∈Z+)交换子MmΩ,α,bMmΩ,α,bf(x)=supr>01rn-α∫|x-y|1,b∈BMO(Rn),且m∈Z+,如果p,q,s,ω满足下述条件之一,那么存在与f无关的常数C,使得‖MmΩ,α,bf‖q,ωq≤C‖f‖p,wp(i)s>q,ω-s’∈A(q’s’,p’s’);(ii)αn+1s<1p<1s’,存在1

Weighted boundedness of commutators of maximal operators with rough kernels

For commutators MmΩ,α,b,defined by MmΩ,α,b f(x)=supr>01rn-α∫|x-y|1,b∈BMO(Rn) and m∈Z+,if p,q,s and ω satisfy one of the following two conditions,then there exits a constant C independent of f such that(i)s>q,ω-s′∈A(q′s′,p′s′) (ii)αn+1s<1p<1s′,there exits 1