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1.
In this paper we study some improvements of the classical Hardy inequality. We add to the right hand side of the inequality
a term that depends on some Lorentz norms of u or of its gradient and we find the best values of the constants for remaining terms. In both cases we show that the problem
of finding the optimal value of the constant can be reduced to a spherically symmetric situation. This result is new when
the right hand side is a Lorentz norm of the gradient. 相似文献
2.
In this paper, we consider Carlson type inequalities and discuss their possible improvement. First, we obtain two different types of generalizations of discrete Carlson's inequality by using the Hlder inequality and the method of real analysis, then we combine the obtained results with a summation formula of infinite series and some Mathieu type inequalities to establish some improvements of discrete Carlson's inequality and some Carlson type inequalities which are equivalent to the Mathieu type inequalities. Finally, we prove an integral inequality that enables us to deduce an improvement of the Nagy-Hardy-Carlson inequality. 相似文献
3.
通过引入两对共轭指数,一个独立参数与权函数,建立一个新的逆向Hilbert型积分不等式及其等价式.并证明了其常数因子为最佳值.作为本文结论的特殊情形,得到了一个经典的Hilbert型积分不等式的含参数s,t的逆向式. 相似文献
4.
Potential Analysis - In this paper, we prove several improvements for the sharp singular Moser–Trudinger inequality. We first establish an improved singular Moser–Trudinger inequality... 相似文献
5.
较为精密的Hardy-Hilbert等式的一个加强 总被引:12,自引:2,他引:10
本文证明了如下权系数的不等式:这里,(C为Euler常数).从而建立了一个加强的Hardy-Hilbert不等式,并建立了一个新的Hardy-Hilbert类不等式及其加强式. 相似文献
6.
We prove a general duality result showing that a Brascamp–Lieb type inequality is equivalent to an inequality expressing subadditivity of the entropy, with a complete correspondence of best constants and cases of equality. This opens a new approach to the proof of Brascamp–Lieb type inequalities, via subadditivity of the entropy. We illustrate the utility of this approach by proving a general inequality expressing the subadditivity property of the entropy on ${\mathbb {R}^n}We prove a general duality result showing that a Brascamp–Lieb type inequality is equivalent to an inequality expressing subadditivity
of the entropy, with a complete correspondence of best constants and cases of equality. This opens a new approach to the proof
of Brascamp–Lieb type inequalities, via subadditivity of the entropy. We illustrate the utility of this approach by proving
a general inequality expressing the subadditivity property of the entropy on
\mathbb Rn{\mathbb {R}^n}, and fully determining the cases of equality. As a consequence of the duality mentioned above, we obtain a simple new proof
of the classical Brascamp–Lieb inequality, and also a fully explicit determination of all of the cases of equality. We also
deduce several other consequences of the general subadditivity inequality, including a generalization of Hadamard’s inequality
for determinants. Finally, we also prove a second duality theorem relating superadditivity of the Fisher information and a
sharp convolution type inequality for the fundamental eigenvalues of Schr?dinger operators. Though we focus mainly on the
case of random variables in
\mathbb Rn{\mathbb {R}^n} in this paper, we discuss extensions to other settings as well. 相似文献
7.
Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules. 相似文献
8.
Mojtaba Bakherad 《Linear and Multilinear Algebra》2019,67(5):871-885
In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method. 相似文献
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10.
New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator Pólya-Szegö inequality to arbitrary operator means. Furthermore, we obtain some new lower and upper bounds for the Tsallis relative operator entropy, operator monotone functions and positive linear maps. 相似文献
11.
Generalized Logan’s Problem for Entire Functions of Exponential Type and Optimal Argument in Jackson’s Inequality in <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>(ℝ<Superscript>3</Superscript>)
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We study Jackson's inequality between the best approximation of a function f ∈ L2(R3) by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson's inequality with the exact constant and the optimal argument in the modulus of continuity. In particular, Jackson's inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue-Morse modulus of continuity of order r ∈ N. These results are based on the solution of the generalized Logan problem for entire functions of exponential type. For it we construct a new quadrature formulas for entire functions of exponential type. 相似文献
12.
In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem. 相似文献
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14.
We prove a Harnack inequality for positive harmonic functions on graphs which is similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean value inequality of nonnegative subharmonic functions on graphs. 相似文献
15.
给出了齐型空间上Lipschitz函数空间的两个新的等价范数,证明了Lipschitz函数满足与BMO函数类似的Joho-Nirenberg型不等式. 相似文献
16.
多元样本定理及混淆误差的估计 总被引:13,自引:0,他引:13
本文证明了多元指数型整函数的一个Marcinkiewica型不等式,并由此证得了多元Whittaker-Kotelnikov-Shannon型的样本定理,从而得到了多元Sobolev类上的混淆误差界的阶的精确估计。 相似文献
17.
《中国科学 数学(英文版)》2017,(5)
We study the Cauchy problem of a semilinear parabolic equation. We construct an appropriate Harnack quantity and get a differential Harnack inequality. Using this inequality, we prove the finite-time blow-up of the positive solutions and recover a classical Harnack inequality. We also obtain a result of Liouville type for the elliptic equation. 相似文献
18.
In this paper we prove a Hermite–Hadamard type inequality for fuzzy integrals. Some examples are given to illustrate the results. 相似文献
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20.
In this paper we define the Jensen–Steffensen inequality and its converse for diamond integrals. Then we give some improvements of these inequalities using Taylor’s formula and the Green function. We investigate bounds for the identities related to improvements of the Jensen–Steffensen inequality and its converse. 相似文献