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Let Mα be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D∞,σ=v-1/(p-1)∈A∞. The boundedness of Mα on some homogenous groups (G,‖·‖,dx) and the covering Lemma of Calderon-Zygmund type are studied. Not only an adequate covering Lemma of Calderon-Zygmund type is shown, but also the boundedness of fractional maximal operators Mα(0<α≤1) on some of homogeneous groups with respect to a given pair of weight functions (u,v) as above is proved. Moreover, a sufficient and necessary condition for Mα∈B(uqdx,vpdx), 0<α<1, 1<p<(1)/(α), and (1)/(q)=(1)/(p)-α is also given. Finally, an application of the results is also obtained. 相似文献
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