相关论文: Further improvements of Young inequality
We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.
We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.
This is a comprehensive set of notes on the ArXiV paper math.CA/0609815 by Dmitry Bilyk and the author. The focus of that paper is a new inequality for sums of hyperbolic Haar functions in three variables, extending a famous result of J…
We prove some new retarded integral inequalities. The results generalize those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].
We give an "elementary" proof of an inequality due to Maz'ya. As a prerequisite we prove an approximation property for the Hausdorff measure. We also comment on the relations between Maz'ya's inequality, the isoperimetric inequality and the…
Certain smoothing inequalities were proposed in the recent paper posted on arXiv at arxiv:1301.2828 in order to lessen the very large gap between the best correctly established upper and lower bounds on the constant factor in the nonuniform…
We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66…
Using well-known techniques, we establish Hardy-Littlewood-type and Hausdorff-Young-type inequalities for generalized Gegenbauer expansions and their unification.
We give new lower asymptotical estimate of constant \[ C_n=\sup\biggl\{\frac{\|t_n\|_{C(\mathbb T)}}{\|t_n\|_{L(\mathbb T)}}:t_n\text{are real trigonometric polynomials}, \operatorname{deg}t_n<n\biggr\} \] as $n\to\infty$. This estimate…
We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and G\"{o}tze. Under mild assumptions the condition is also necessary.…
In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob's inequality for submartingale and Kolmogrov's inequality. By Kolmogrov's inequality, we obtain a special version of Kolmogrov's law of…
In this paper, new upper and lower bounds for the Trapezoid inequality of absolutely continuous functions are obtained. Applications to some special means are provided as well.
In this paper, we first establish a version of multidimensional analogues of the refined Bohr's inequality. Then we establish two versions of multidimensional analogues of improved Bohr's inequality with initial coefficient being zero.…
In this current work, we revisit the recent improvement of the discrete Hardy's inequality in one dimension and establish an extended improved discrete Hardy's inequality with its optimality. We also study one-dimensional discrete Copson's…
This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional…
The purpose of this note is to provide a detailed proof of Nazarov's inequality stated in Lemma A.1 in Chernozhukov, Chetverikov, and Kato (2017, Annals of Probability).
In this article, we establish an improvement of the Cauchy-Schwarz inequality. Let $x, y \in \mathcal{H},$ and let $f: (0,1) \rightarrow \mathbb{R}^+$ be a well-defined function, where $\mathbb{R}^+$ denote the set of all positive real…
In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.