The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H...The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.展开更多
Tarnavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequslity was derived in this paper. As its applications, some separations of other inequalities were given.
In the present paper, we answer the question: for 0a what are the greatest value p(a) and the least value q(a) such that the double inequality Jp(a,b)aA(a,b)+ (1-a)G(a,b)Jq(a,b) holds for all a,b>0 with a is not eq...In the present paper, we answer the question: for 0a what are the greatest value p(a) and the least value q(a) such that the double inequality Jp(a,b)aA(a,b)+ (1-a)G(a,b)Jq(a,b) holds for all a,b>0 with a is not equal to?b ?展开更多
In the present paper, we answer the question: for 0 what are the greatest value p(a) and the least value q(a) such that the inequality. For more information about abstract,please download the PDF file.
In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for t...In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.展开更多
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for...Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for corresponding semigroup. Moreover, a Dresher＇s type inequality for two-parameter family of means, is also proved.展开更多
The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.
Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite a...Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite and can be attained.This partially generalizes a well-known work of Chang and Yang(1988)who have obtained the inequality whenβ=0.展开更多
We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respe...We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:展开更多
The assay argues that the Equality-Inequality dialectics is a very complex issue,which reflects many social dilemmas.On one side are the state official commitments to secure,maintain and protect all kinds of formal eq...The assay argues that the Equality-Inequality dialectics is a very complex issue,which reflects many social dilemmas.On one side are the state official commitments to secure,maintain and protect all kinds of formal equalities.On the other side are the natural and genetic distinctions that differ between human-beings while creating and maintaining inequality.In fact,this is kind of a contradiction exists in many fields of social sciences.The essay’s author reviews some of the relevant historical events,such as social mobility,individualism and education and points out on future solutions.Among the proposed suggestions are:1)Embracing Frankl’s giving“Meaning to Life”as a leverage for increasing pleasure of life;2)Recognizing and promoting Creative Individualism as the legitimized ground for inequality;3)Increasing Social Cohesion,required for social empowerment and attaining security and happiness.展开更多
We prove a Harnack inequality for positive harmonic functions on graphs whichis similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean valueinequality of nonnegative subharmonic functions ...We prove a Harnack inequality for positive harmonic functions on graphs whichis similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean valueinequality of nonnegative subharmonic functions on graphs.展开更多
In this paper,we prove a sharp anisotropic L;Minkowski inequality involving the total L^(p)anisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in R^(n).As consequence...In this paper,we prove a sharp anisotropic L;Minkowski inequality involving the total L^(p)anisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in R^(n).As consequences,we obtain an anisotropic Willmore inequality,a sharp anisotropic Minkowski inequality for outward F-minimising sets and a sharp volumetric anisotropic Minkowski inequality.For the proof,we utilize a nonlinear potential theoretic approach which has been recently developed by Agostiniani et al.(2019).展开更多
We provide some lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality in terms of the so-called Stein characterization of the Gaussian distribution.The techniques are based on the representation o...We provide some lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality in terms of the so-called Stein characterization of the Gaussian distribution.The techniques are based on the representation of the relative Fisher information along the Ornstein-Uhlenbeck semigroup by the Minimum Mean-Square Error from information theory.展开更多
It is well known that for almost all real number x, the geometric mean of the first n digits di（x） in the Lüroth expansion of x converges to a number K0 as n→∞. On the other hand, for almost all x, the arithm...It is well known that for almost all real number x, the geometric mean of the first n digits di（x） in the Lüroth expansion of x converges to a number K0 as n→∞. On the other hand, for almost all x, the arithmetric mean of the first n Lüroth expansion digits di（x） approaches infinity as n→∞. There is a sequence of refinements of the AM-GM inequality, Maclaurin＇s inequalities, relating the 1/k-th powers of the k-th elementary symmetric means of n numbers for 1≤k≤n. In this paper, we investigate what happens to the means of Lüroth expansion digits in the limit as one moves f（n） steps away from either extreme. We prove sufficient conditions on f（n） to ensure divergence when one moves away from the arithmetic mean and convergence when one moves f（n） steps away from geometric mean.展开更多
基金supported by project TMOP-4.2.2.A-11/1/KONV-2012-0051,Shota Rustaveli National Science Foundation grant no.13/06(Geometry of function spaces,interpolation and embedding theorems)
文摘The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.
基金Project supported by National Natural Science Foundation of China （Grant No. 10271071）
文摘Tarnavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequslity was derived in this paper. As its applications, some separations of other inequalities were given.
文摘In the present paper, we answer the question: for 0a what are the greatest value p(a) and the least value q(a) such that the double inequality Jp(a,b)aA(a,b)+ (1-a)G(a,b)Jq(a,b) holds for all a,b>0 with a is not equal to?b ?
文摘In the present paper, we answer the question: for 0 what are the greatest value p(a) and the least value q(a) such that the inequality. For more information about abstract,please download the PDF file.
基金Foundation item： Supported by the Scientific Research Common Program of Beijing Municipal Commission of Education of China（Km200611417009） Suppoted by the Natural Science Foundation of Fujian Province Education Department of China（JA05324）
文摘In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.
文摘In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
文摘Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for corresponding semigroup. Moreover, a Dresher＇s type inequality for two-parameter family of means, is also proved.
基金the Scientific Research fund of Pingyuan University(2005006)
文摘The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.
基金supported by National Natural Science Foundation of China(Grant Nos.11721101 and 11401575)。
文摘Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite and can be attained.This partially generalizes a well-known work of Chang and Yang(1988)who have obtained the inequality whenβ=0.
文摘We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:
文摘The assay argues that the Equality-Inequality dialectics is a very complex issue,which reflects many social dilemmas.On one side are the state official commitments to secure,maintain and protect all kinds of formal equalities.On the other side are the natural and genetic distinctions that differ between human-beings while creating and maintaining inequality.In fact,this is kind of a contradiction exists in many fields of social sciences.The essay’s author reviews some of the relevant historical events,such as social mobility,individualism and education and points out on future solutions.Among the proposed suggestions are:1)Embracing Frankl’s giving“Meaning to Life”as a leverage for increasing pleasure of life;2)Recognizing and promoting Creative Individualism as the legitimized ground for inequality;3)Increasing Social Cohesion,required for social empowerment and attaining security and happiness.
基金supported by the National Science Foundation of China(11671401)
文摘We prove a Harnack inequality for positive harmonic functions on graphs whichis similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean valueinequality of nonnegative subharmonic functions on graphs.
基金supported by National Natural Science Foundation of China(Grant No.11871406)。
文摘In this paper,we prove a sharp anisotropic L;Minkowski inequality involving the total L^(p)anisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in R^(n).As consequences,we obtain an anisotropic Willmore inequality,a sharp anisotropic Minkowski inequality for outward F-minimising sets and a sharp volumetric anisotropic Minkowski inequality.For the proof,we utilize a nonlinear potential theoretic approach which has been recently developed by Agostiniani et al.(2019).
基金Grants No.F1R-MTH-PUL-15CONF and No. F1R-MTH-PUL-15STAR at Luxembourg University
文摘We provide some lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality in terms of the so-called Stein characterization of the Gaussian distribution.The techniques are based on the representation of the relative Fisher information along the Ornstein-Uhlenbeck semigroup by the Minimum Mean-Square Error from information theory.
基金Supported by the National Natural Science Foundation of China(11271148)
文摘It is well known that for almost all real number x, the geometric mean of the first n digits di（x） in the Lüroth expansion of x converges to a number K0 as n→∞. On the other hand, for almost all x, the arithmetric mean of the first n Lüroth expansion digits di（x） approaches infinity as n→∞. There is a sequence of refinements of the AM-GM inequality, Maclaurin＇s inequalities, relating the 1/k-th powers of the k-th elementary symmetric means of n numbers for 1≤k≤n. In this paper, we investigate what happens to the means of Lüroth expansion digits in the limit as one moves f（n） steps away from either extreme. We prove sufficient conditions on f（n） to ensure divergence when one moves away from the arithmetic mean and convergence when one moves f（n） steps away from geometric mean.
