### Abstract

Let p < 1, 1/p + 1/p^{*} = 1, and a = (a_{n}) _{n=1}∞, b = (b_{m})m_{=1}∞ be two complex sequences. We exhibit the generalization of Hardy-Hilbert's inequality of the following type: (eqution presented) where K: (0, ∞) × (0, ∞) → (0, ∞), f_{1}, f_{2}, φ_{1}, φ_{2}: (0, ∞) → (0, ∞_{1}) and C is a suitable constant. We also get several interesting inequalities which generalize many recent results.

Original language | English |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Mathematical Inequalities and Applications |

Volume | 14 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2011 |

### Keywords

- Hardy-Hilbert's inequality
- Hilbert's inequality
- Inequalities

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## Cite this

Chang, C. T., Lan, J. W., & Wang, K-Z. (2011). A new generalization of Hardy-Hilbert's inequality with non-homogeneous kernel.

*Mathematical Inequalities and Applications*,*14*(1), 1-11. https://doi.org/10.7153/mia-14-01