关于Marcinkiewicz积分交换子的一点注记

Note on commutator of Marcikiewicz integral

利用类似Plauszynski相应定理的证明方法,研究了一类Marcinkiewicz积分交换子的性质,证明了当b∈Λ·β时,设1<p<∞,0<β<1,1β时,Maricinkiewicz积分交换子Cb(f)的Lq(Rn)到Lp(Rn)的有界性,即当b∈Λ·p-1‖f‖Lp.n,则有‖Cbf(x)

Similar to the method of correponding theorm of Plauszynski, the properties of a class of Marcinkiewicz integral commutator generated by Λ·_β functions are studied, and the boundedness of this class of Marcinkiewicz integral commutator C_bf from L^q(R^n) to L^p(R^n) when b∈Λ·_β is proved, i.e. when b∈Λ·_β, and 1<p<∞, 0<β<1, 1p-1q=βn, then ‖C_bf(x)‖_(L^q)≤C‖b‖_(Λ·_β)‖f‖_(L^p).