Results 221 to 228 of about 359 (228)
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2021
A quantitative stability result with an optimal exponent is established, concerning near-maximizers for Young’s convolution inequality for Euclidean groups.
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A quantitative stability result with an optimal exponent is established, concerning near-maximizers for Young’s convolution inequality for Euclidean groups.
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REMARKS ON THE HAUSDORFF-YOUNG INEQUALITY
2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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An Operation Connected to a Young‐Type Inequality
Mathematische Nachrichten, 1992AbstractGiven two φ‐functions F and G we consider the largest φ‐function H = F ⊕ G such that the Young‐type inequality H(xy) ⩽ F(x) + G(y) holds for all x, y > 0. We prove an equivalence theorem for F ⊕ G with the best constants and, for the special case when F and G are log‐convex and satisfy a certain growth condition, a representation formula for
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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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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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