Note on Hölder inequalities

In this note, we show that if m,n are positive integers and xij≥0, for i=1,…,n, for j=1,…,m, then (∑i=1nxi1⋯xim)m≤(∑i=1nxi1m)⋯(∑i=1nximm) with equality, in case (x11,⋯,xn1)≠0 if and only if each vector (x1j,⋯,xnj), j=1,⋯,m, is a scalar multiple of (x11,⋯,xn1). The proof is a straight-forward applica...

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Bibliographic Details
Main Author: Sung Guen Kim
Format: Article
Language:English
Published: Hindawi Limited 1995-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171295000494