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: (eqution presented) where K: (0, ∞) × (0, ∞) → (0, ∞), f1, f2, φ1, φ2: (0, ∞) → (0, ∞1) and C is a suitable constant. We also get several interesting inequalities which generalize many recent results.
- Hardy-Hilbert's inequality
- Hilbert's inequality