Note on Hölder inequalities

Sung Guen Kim

International Journal of Mathematics and Mathematical Sciences, 1995, vol. 18, 1-2

Abstract:

In this note, we show that if m , n are positive integers and x i j ≥ 0 , for i = 1 , … , n , for j = 1 , … , m , then ( ∑ i = 1 n x i 1 ⋯ x i m ) m ≤ ( ∑ i = 1 n x i 1 m ) ⋯ ( ∑ i = 1 n x i m m ) with equality, in case ( x 11 , ⋯ , x n 1 ) ≠ 0 if and only if each vector ( x 1 j , ⋯ , x n j ) , j = 1 , ⋯ , m , is a scalar multiple of ( x 11 , ⋯ , x n 1 ) . The proof is a straight-forward application of Hölder inequalities Conversely, we show that Hölder inequalities can be derived from the above result.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:487947

DOI: 10.1155/S0161171295000494

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