Note on Hölder Inequalities

Sung Guen Kim

doi:10.1155/S0161171295000494

Note on Hölder Inequalities

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Abstract

In this note, we show that if m, n are positive integers and x_ij ≥ 0, for i = l,…., n, for j = 1, …, m, then [formula omitted] with equality, in case (:r₁₁,. ·., x_n1) ≠ 0 if and only if each vector (x_1j · · ·, x_nj), j = 1, ·, m, is a scalar multiple of (x₁₁, ·., x_n1). The proof is a straight-forward application of Hölder inequalities. Conversely, we show that Hölder inequalities can be derived from the above result.

Original language	English
Pages (from-to)	397-398
Number of pages	2
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	18
Issue number	2
DOIs	https://doi.org/10.1155/S0161171295000494
State	Published - 1995

Keywords

The Hölder Inequalities

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10.1155/S0161171295000494

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title = "Note on H{\"o}lder Inequalities",

abstract = "In this note, we show that if m, n are positive integers and xij ≥ 0, for i = l,…., n, for j = 1, …, m, then [formula omitted] with equality, in case (:r11,. ·., 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 application of H{\"o}lder inequalities. Conversely, we show that H{\"o}lder inequalities can be derived from the above result.",

keywords = "The H{\"o}lder Inequalities",

author = "Kim, {Sung Guen}",

year = "1995",

doi = "10.1155/S0161171295000494",

language = "English",

volume = "18",

pages = "397--398",

journal = "International Journal of Mathematics and Mathematical Sciences",

issn = "0161-1712",

publisher = "John Wiley and Sons Ltd",

number = "2",

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T1 - Note on Hölder Inequalities

AU - Kim, Sung Guen

PY - 1995

Y1 - 1995

N2 - In this note, we show that if m, n are positive integers and xij ≥ 0, for i = l,…., n, for j = 1, …, m, then [formula omitted] with equality, in case (:r11,. ·., 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 application of Hölder inequalities. Conversely, we show that Hölder inequalities can be derived from the above result.

AB - In this note, we show that if m, n are positive integers and xij ≥ 0, for i = l,…., n, for j = 1, …, m, then [formula omitted] with equality, in case (:r11,. ·., 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 application of Hölder inequalities. Conversely, we show that Hölder inequalities can be derived from the above result.

KW - The Hölder Inequalities

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DO - 10.1155/S0161171295000494

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VL - 18

SP - 397

EP - 398

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 2

ER -

Note on Hölder Inequalities

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