Results 11 to 20 of about 493,191 (280)
A NEW REFINEMENT OF YOUNG'S INEQUALITY [PDF]
Proceedings of the Edinburgh Mathematical Society, 2007 AbstractA classical theorem due to Young states that the cosine polynomial$$ C_n(x)=1+\sum_{k=1}^{n}\frac{\cos(kx)}{k} $$is positive for all $n\geq1$ and $x\in(0,\pi)$. We prove the following refinement. For all $n\geq2$ and $x\in[0,\pi]$ we have$$ \tfrac{1}{6}+c(\pi-x)^2\leq C_n(x), $$with the best possible constant factor$$ c=\min_{0\leq t\lt\pi ...
Alzer, H. +3 more
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Young's integral inequality with upper and lower bounds
Electronic Journal of Differential Equations, 2011 Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent in this ...
Douglas R. Anderson +2 more
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Linear Algebra and its Applications, 2009 Let \(M_{n}({\mathbb C})\) be the set of all complex \(n\)-square matrices. The modulus \((X^{\ast }X)^{1/2}\) of \(X\in M_{n}\) is written as \(|X|\). Let \(h=h(t):[0,\infty )\rightarrow [ 0,\infty )\) be strictly increasing, continuous function with \( h(0)=0\) and \(h(t)\rightarrow \infty \) as \(t\rightarrow \infty \).
Cho, Kazuki, Sano, Takashi
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The interpolation of Young’s inequality using dyadics
Journal of Inequalities and Applications, 2019 In this article we interpolate Young’s inequality using a delicate treatment of dyadics. Although there are other simple methods to prove these results, we present this new approach hoping to reveal more of the hidden properties of such inequalities.
Mohammad Sababheh, Abdelrahman Yousef
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A refinement of Young’s inequality [PDF]
Acta Mathematica Hungarica, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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New Young Inequalities and Applications [PDF]
Zeitschrift für Analysis und ihre Anwendungen, 2019 We establish upper bounds for the convolution operator acting between interpolation spaces. This gives new Young inequalities in the context of Lorentz–Karamata spaces, grand Lebesgue spaces and small Lebesgue spaces besides many other known results. Furthermore, we use this abstract Young inequality to prove a bilinear interpolation theorem for limit ...
Fernández-Martínez, Pedro +1 more
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On further refinements for Young inequalities
Open Mathematics, 2018 In this paper sharp results on operator Young’s inequality are obtained. We first obtain sharp multiplicative refinements and reverses for the operator Young’s inequality.
Furuichi Shigeru, Moradi Hamid Reza
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Multiple-Term Refinements of Young Type Inequalities
Journal of Mathematics, 2016 Recently, a multiple-term refinement of Young’s inequality has been proved. In this paper, we show its reverse refinement. Moreover, we will present multiple-term refinements of Young’s inequality involving Kantorovich constants.
Daeshik Choi
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Boundary Value Problems, 2022 In this article, we consider a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity. We prove explicit and general decay rate results of the solution to the viscoelastic plate equation with past history.
Bhargav Kumar Kakumani +1 more
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Sharpness in Young’s inequality for convolution [PDF]
Pacific Journal of Mathematics, 1977 Summary: Let \(p\) and \(q\) be indices in the open interval \((1,\infty)\) such that \(pq < p+q\); let \(r = pq/(p+q-pq)\). It is shown here that there is a constant \(C_{p,q} < 1\) such that, if \(G\) is a locally compact, unimodular group with no compact open subgroups, and if \(g\) and \(f\) are functions in \(L^p(G)\) and \(L^q(G)\) respectively ...
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