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Let q be a positive integer. Recently, Niu and Liu proved that, if , then the product is not a powerful number. In this note, we prove (1) that, for any odd prime power ? and , the product is not a powerful number, and (2) that, for any positive odd integer ?, there exists an integer such that, for any positive integer , the product is not a powerful number. 相似文献
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胡国恩 《数学物理学报(B辑英文版)》2005,25(3):545-554
Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the Lp(Rn) boundedness (1<p<∞) and the weak type (H1(Rn), L1(Rn))boundedness for the corresponding commutators. A new interpolation theorem is also established. 相似文献
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