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中文摘要：
研究了粗糙核分数次积分及交换子在Herz型Hardy空间上的加权估计。当Ω∈Ls（Sn-1）（1＜s＜∞）时，利用原子分解证明了粗糙核分数次积分TΩ，l以及由它和BM痹O函数生成的交换子[ b，TΩ，l ]是从加权Herz型Hardy空间到（弱）加权Herz空间上有界的。同时，对粗糙核分数次极大算子也得到了相应的结果。
英文摘要：
The main goal of this paper is to study the weighted estimates about the fractional integrals with rough kernels and its commutators on the Herz-type Hardy spaces.AsΩ∈Ls（Sn-1）（1〈s〈∞）, it is proved that the fractional inte-grals TΩ,l and its commutators [ b,TΩ,l ] generated by the BMO functions are bounded from the weighted Herz-type Har-dy spaces to the weighted Herz spaces by using the atomic decompositions.Also, the corresponding results are also obtained for the maximal fractional integrals with rough kernels.
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