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A Multilinear Young's Inequality
Canadian Mathematical Bulletin, 1988AbstractWe prove an (n + l)-linear inequality which generalizes the classical bilinear inequality of Young concerning the LP norm of the convolution of two functions.
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International Journal of Mathematical Education in Science and Technology, 1994
Our aim is to present a completed form of Young's inequality. We will give an elementary analytic proof of this inequality by the application of the mean value theorem for integrals known from a first course in real analysis. Moreover, to facilitate understanding, the heuristic strategy of analogy, which is a constructive source of discovery, will be ...
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Our aim is to present a completed form of Young's inequality. We will give an elementary analytic proof of this inequality by the application of the mean value theorem for integrals known from a first course in real analysis. Moreover, to facilitate understanding, the heuristic strategy of analogy, which is a constructive source of discovery, will be ...
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International Journal of Mathematical Education in Science and Technology, 2004
In this paper, an error in a well-known work which claims to prove Young's inequality is discovered and a concise proof of Young's inequality is given.
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In this paper, an error in a well-known work which claims to prove Young's inequality is discovered and a concise proof of Young's inequality is given.
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Companions of the inequalities of Fejér--Jackson and Young
Analysis Mathematica, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alzer, H. +3 more
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Weighted Young Inequalities for Convolutions
Southeast Asian Bulletin of Mathematics, 2003Let \(1 < p, q < \infty\) 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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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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Further refinements of Young’s type inequality for positive linear maps
RACSAM, 2021M. Ighachane, M. Akkouchi
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REMARKS ON THE HAUSDORFF-YOUNG INEQUALITY
2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Characterization of the trace by Young's inequality
2005Let \(\varphi\) 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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Sharpness in Young's Inequality for Convolution Products
Canadian Journal of Mathematics, 1994AbstractSuppose 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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