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Some new Carleman-Knopp type inequalities are proved as "end point" inequalities of modern forms of Hardy's inequalities. Both finite and infinite intervals are considered and both the cases p q and q p are investigated. The obtained results are compared with similar results in the literature and the sharpness of the constants is discussed for the power weight case. Moreover, some reversed Carleman-Knopp inequalities are derived and applied.

Carleman-Knopp type inequalities via Hardy inequalities