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Companions of the inequalities of Fejér--Jackson and Young

Analysis Mathematica, 2005
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Alzer, H.   +3 more
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Weighted Young Inequalities for Convolutions

Southeast Asian Bulletin of Mathematics, 2003
Let \(1 < p, q < \infty\) and let \(u\) and \(v\) be weighted functions on \(\mathbb R^n\). The aim of the paper is to find sufficient conditions for the validity of the inequality \[ \Bigl(\int_{\mathbb R^n} (g \times f)^q (x)\, u (x) \, dx\Bigr)^{1/q} \leq C \| g\| _X \Bigl(\int_{\mathbb R^n} f (x)^p \, v (x) \, dx\Bigr)^{1/p} \] for all measurable ...
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REMARKS ON THE HAUSDORFF-YOUNG INEQUALITY

2000
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Characterization of the trace by Young's inequality

2005
Let \(\varphi\) be a positive linear functional on the algebra of complex matrices of order \(n\) and \(p, q\) be positive numbers such that \(1/p + 1/q = 1\). It is shown that if \(\varphi(| AB| ) \leqslant (1/p) \varphi(A^p)+(1/q) \varphi(B^q)\) holds for any positive semi-definite matrices \(A, B\), then \(\varphi\) is a positive scalar multiple of ...
Bikchentaev A., Tikhonov O.
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Matrix Young Inequalities

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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Sharpness in Young's Inequality for Convolution Products

Canadian Journal of Mathematics, 1994
AbstractSuppose that Gis a locally compact group with modular function Δ and that p, q, r are three numbers in the interval (l,∞) satisfying. If cp,q(G) is the smallest constant c such thatfor all functions f, g ∈ Cc(G) (here the convolution product is with respect to left Haar measure andis the exponent which is conjugate to p) then Young's inequality
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Presentation of Young's inequality [PDF]

open access: possibleJournal 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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