【摘要】 设 f(x)∈Lp(0 ,∞ ) ,p >1及 f(x)≥ 0 .Hardy证明了∫∞0(∫x0 f(t)dt x) pdx≤ (p/ (p - 1) ) p∫∞0 fp(x)dx ,此不等式叫Hardy不等式 .后来Hardy又给出两种不同的推广 ,该文目的在给出的Hardy已推广的不等式的基础上再推广并予以改进 .更多还原

【Abstract】 Let f(x)∈L-p (0,∞),p>1 and f(x) ≥0.Hardy proved that ∫-∞ 0(∫-x 0f(t)dt/x)-pdx≤ (p/(p-1))-p∫-∞ 0f-p(x)dx. This inequality is called Hardy’s inequality.After some years,Hardy gave two dif ferent extensions of this inequality.In this paper, the two generalized inequali tes of Hardy’s extensions of this inequality are improved.更多还原