International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 397-398
Note on Hölder inequalities
Department of Mathematics, Pohang Institute of Science & Technology, P.O. Box 215, Pohang, 790-600, Korea
Received 13 April 1992; Revised 26 June 1993
Copyright © 1995 Sung Guen Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this note, we show that if are positive integers and , for
, for , then
with equality, in case if and only if each vector , , is
a scalar multiple of . The proof is a straight-forward application of Hölder
inequalities Conversely, we show that Hölder inequalities can be derived from the above result.