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1995
Let p, q > 0 satisfy 1/p + 1/q = 1. We prove that for any pair A, B of n × n complex matrices there is a unitary matrix U, depending on A, B, such that $$U*\left| {AB*} \right|U \leqslant {\left| A \right|^p}/p + {\left| B \right|^q}/q.$$
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Let p, q > 0 satisfy 1/p + 1/q = 1. We prove that for any pair A, B of n × n complex matrices there is a unitary matrix U, depending on A, B, such that $$U*\left| {AB*} \right|U \leqslant {\left| A \right|^p}/p + {\left| B \right|^q}/q.$$
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Presentation of Young's inequality [PDF]
Journal of inequalities and special functions, 2015 The paper presents different forms of Young's inequality. Main results include generalizations of the discrete and integral form. Issues on inequalities are studied using the geometric-arithmetic mean inequality, integral method and Jensen's inequality. A functional approach to Young's inequality is also considered.
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A Generalization of Young’s Inequality
1987A function φ: [0, ∞) → [0, ∞) is said to be a Young function if (i) φ is increasing and right continuous on [0, ∞) (ii) $$\mathop {\lim }\limits_{x \to \infty } {\mkern 1mu} \phi ({\text{x}}){\text{ = }}\infty .$$
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Extremal pairs of Young’s inequality for Kac algebras
, 2018Zheng-Wei Liu, Jin-Song Wu
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An analog of Young’s inequality for convolutions of functions for general Morrey-type spaces
, 2016V. Burenkov, T. Tararykova
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Inequities in adolescent and young adult deaths
The Lancet, 2021Shanthi, Ameratunga, Asha, George
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2006
Operator and matrix versions of classical inequalities are of considerable interest in mathematics. A fundamental inequality among positive real numbers is the arithmetic-geometric mean inequality whose generalization is the most important case of the Young inequalities.
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Operator and matrix versions of classical inequalities are of considerable interest in mathematics. A fundamental inequality among positive real numbers is the arithmetic-geometric mean inequality whose generalization is the most important case of the Young inequalities.
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