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A GENERALIZATION OF HÖLDER AND MINKOWSKI INEQUALITIES

In this work, we give a generalization of Hölder and Minkowski inequalities to normal sequence algebras with absolutely monotone seminorm. Our main result is Theorem 2.1 and Theorem 2.2 which state these extensions. Taking F = `1 and ‖·‖F = ‖·‖1 in both these theorems, we obtain classical versions of these inequalities. Also, using these generalizations we construct the vector-valued sequence space F (X, λ, p) as a paranormed space which is a most general form of the space c0 (X, λ, p) investigated in [6].