加权Hardy-Littlewood平均算子的交换子在Herz型空间的有界性

THE BOUNDEDNESS OF COMMUTATOR ASSOCIATED TO WEIGHTED HARDY-LITTLEWOOD AVERAGE OPERATOR IN HERZ-TYPE SPACE

主要讨论了加权Hardy-Littlewood平均算子Uψ与BMO函数b生成的交换子在Herz型空间和Morrey型Herz空间上的有界性,并给出了其在Morrey型Herz空间上有界的充分条件是∫01t-(α+n/q2-l)ψ(t)log2tdt<∞.若α=0,l=0,q1=q2=p>1,则∫01t-(α+n/q2-l)ψ(t)log2tdt=∫01t-n/pψ(t)log2tdt<∞,此时交换子Ubψ是Lp(Rn)空间上的有界算子.

The boundedness of commutator Uψb generated by the Weighted Hardy-Littlewood average operator U and BMO function b in Herz and Morrey-Herz type spaces are discussed.It is showed that the sufficient condition for its boundedness in the Morrey-Herz type spaces is ∫10t-（α＋n/q2-1）ψ（t）log2tdt∞.It turned to be ∫10t-n/pψ（t）log2tdt∞ as α=0,1=0 and q1=q2=p1,and then Uψb is bounded on Lp（Rn）.