Landau's converse to H\" older's inequality
Abstract
By H\" older's inequality, if x ∈ p, then xy ∈ 1 for all y ∈ q. Landau proved the converse result: If xy ∈ 1 for all y ∈ q, then x ∈ p. This paper proves Landau's theorem and considers a related problem for Hilbert's inequality.
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