【摘要】 设[b,T]表示由Lipschitz函数b∈Lipβ(Rn)与满足一定光滑条件的带θ型核的线性算子T生成的交换子,本文研究这类算子在Hardy空间和Herz型Hardy空间上的有界性问题.利用Hardy空间和Herz型Hardy空间的原子分解,证明了当nn+β<p≤1且1n时,交换子[b,T]是从Hp(Rn)到Lq(Rn)有界的;同时当α,q,q1,q2,满足一定q=1p-β(Rn)有界的.条件时,[b,T]是从H Kα,p(Rn)到 Kα,pq1q2更多还原

【Abstract】 let  be commutators generated by Lipsch itz functions b∈Lipβ(Rn) and a linear operator T with a kernel b eing of some smooth conditions. We studied the boundedne ss of the c ommutators on Hardy spaces and Herz-type Hardy spaces by using their atom characterization. The results show that if nn+β<p≤1 and 1q=1p-βn, then  is bounded from Hp(Rn) to Lq(Rn); and if α,q,q 1,q2 satisfy some conditions, then  is bounded from Hα,pq1(Rn) to α,pq2(Rn). 更多还原