A NEW GENERALIZATION OF HARDY–HILBERT’S INEQUALITY WITH NON–HOMOGENEOUS KERNEL

@inproceedings{Chang2011ANG,
  title={A NEW GENERALIZATION OF HARDY–HILBERT’S INEQUALITY WITH NON–HOMOGENEOUS KERNEL},
  author={Chi-Tung Chang and J Q Lan and Kuo-Zhong Wang},
  year={2011}
}
Let p > 1 , 1/p + 1/p∗ = 1 , and a = (an)n=1 , b = (bm) ∞ m=1 be two complex sequences. We exhibit the generalization of Hardy-Hilbert’s inequality of the following type: ∑ n,m 1 K(φ1(n),φ2(m))|an||bm| < C ( ∞ ∑ n=1 | an f1(φ1(n)) |p ) 1 p ( ∞ ∑ m=1 | bm f2(φ2(m)) |p ) 1 p∗ , where K : (0,∞)× (0,∞) → (0,∞) , f1, f2,φ1,φ2 : (0,∞) → (0,∞) and C is a suitable constant. We also get several interesting inequalities which generalize many recent results. Mathematics subject classification (2010… CONTINUE READING

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