An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of c...An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.展开更多
In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic...In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.展开更多
In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies ...In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies the Orlicz Busemann-Petty centroid inequality of Lutwak,Yang and Zhang[23].展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable expo...In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.展开更多
We consider the problem about the space embedded by the space and the embedding inequality. With the HSlder inequality and interpolation inequality, we give the proof of the space embedding theorem and the space holde...We consider the problem about the space embedded by the space and the embedding inequality. With the HSlder inequality and interpolation inequality, we give the proof of the space embedding theorem and the space holder embedding theorem.展开更多
As a generalization of grand Furuta inequality,recently Furuta obtain:If A≥ B≥0 with A>0,then for t∈[0,1]and p1,p2,p3,p4≥1, A t 2[A- t 2{A t 2(A/ t 2 Bp 1A /t2 )p 2A t 2}p 3A /t2 ]p 4A t 2 1 [{(p1/t)p2+t}p3-t]p...As a generalization of grand Furuta inequality,recently Furuta obtain:If A≥ B≥0 with A>0,then for t∈[0,1]and p1,p2,p3,p4≥1, A t 2[A- t 2{A t 2(A/ t 2 Bp 1A /t2 )p 2A t 2}p 3A /t2 ]p 4A t 2 1 [{(p1/t)p2+t}p3-t]p4+t]≤A. In this paper,we generalize this result for three operators as follow:If A≥B≥C≥0 with B>0,t∈[0,1]and p1,p2,···,p2n/1,p2n≥1 for a natural number n.Then the following inequalities hold for r≥t, A1/t+r≥ [A r 2[B /t 2{B t 2······[B /t 2{B t 2(B /t 2 ←B /t 2 n times Bt 2 n/1 times by turns Cp 1B /t 2)p 2B t 2}p 3B /t 2]p 4···B t 2}p 2n/1B /t 2 B /t 2 n times Bt 2 n/1 times by turns→ ]p 2nA r 2] 1/t+r q[2n]+r/t, where q[2n]≡{···[{[(p1/t)p2+t]p3/t}p4+t]p5/···/t}p2n+t /t and t alternately n times appear .展开更多
A generalized Rosenthal＇s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexi...A generalized Rosenthal＇s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.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.
In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.
This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measur...This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.展开更多
We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey sp...We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob＇s inequality on martingale block spaces, we obtain the Davis＇ decompositions for martingale Morrey spaces.展开更多
This paper gives a new generalization of Hilbert＇s inequality with a best constant factor involving the β function. An applications, we consider the equivalent form and some particular results.
Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some suf...Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.展开更多
Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this pa...Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this paper,we investigate the relative positive center set of planar convex bodies.As an application of the relative positive center,we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.展开更多
Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the socalled multivariate weighted Bernstein, Nikol＇skii, an...Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the socalled multivariate weighted Bernstein, Nikol＇skii, and Ul＇yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol＇skii-type and Ul＇yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.展开更多
A new improvement of Hilbert's inequality for double series can be establishedby means of a strengthened Cauchy's inequality. As application, a quite sharp result onFejer-Riesz's inequality is obtained.
基金supported by the NSFC(12171378)supported by the Characteristic innovation projects of universities in Guangdong province(2023K-TSCX381)+3 种基金supported by the Young Top-Talent program of Chongqing(CQYC2021059145)the Major Special Project of NSFC(12141101)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937).
文摘An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
文摘In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.
基金Supported in part by NSFC(12071378,12461009),20XLB012,KJQN202100527,CSTB2022NSCQ-MSX0259 and KJQN202300557.
文摘In this paper,the Orlicz centroid function for log-concave functions is introduced.A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained.The rearrangement inequality implies the Orlicz Busemann-Petty centroid inequality of Lutwak,Yang and Zhang[23].
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
基金supported by NSFC(11471251)supported by NSFC(11271293)
文摘In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.
基金Supported by Soft Science Project of Henan Province(072102210020)
文摘We consider the problem about the space embedded by the space and the embedding inequality. With the HSlder inequality and interpolation inequality, we give the proof of the space embedding theorem and the space holder embedding theorem.
基金Supported by the Science Foundation of Ministry of Education of China（208081） Supported by the Natural Science Foundation of Henan Province（102300410012 2007110016 2008B110006）
文摘As a generalization of grand Furuta inequality,recently Furuta obtain:If A≥ B≥0 with A>0,then for t∈[0,1]and p1,p2,p3,p4≥1, A t 2[A- t 2{A t 2(A/ t 2 Bp 1A /t2 )p 2A t 2}p 3A /t2 ]p 4A t 2 1 [{(p1/t)p2+t}p3-t]p4+t]≤A. In this paper,we generalize this result for three operators as follow:If A≥B≥C≥0 with B>0,t∈[0,1]and p1,p2,···,p2n/1,p2n≥1 for a natural number n.Then the following inequalities hold for r≥t, A1/t+r≥ [A r 2[B /t 2{B t 2······[B /t 2{B t 2(B /t 2 ←B /t 2 n times Bt 2 n/1 times by turns Cp 1B /t 2)p 2B t 2}p 3B /t 2]p 4···B t 2}p 2n/1B /t 2 B /t 2 n times Bt 2 n/1 times by turns→ ]p 2nA r 2] 1/t+r q[2n]+r/t, where q[2n]≡{···[{[(p1/t)p2+t]p3/t}p4+t]p5/···/t}p2n+t /t and t alternately n times appear .
基金Supported by the Scientific Research Foundation of Hubei Province (D200613001)the National Natural Science Foundation of China (10371093)
文摘A generalized Rosenthal＇s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.
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In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.
基金supported by the National Natural Science Foundation of China(11471230,11671282)。
文摘This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.
文摘We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob＇s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob＇s inequality on martingale block spaces, we obtain the Davis＇ decompositions for martingale Morrey spaces.
基金Supported by the NSF of Guangdong Institutions of Higher Learning, College and University(0177).
文摘This paper gives a new generalization of Hilbert＇s inequality with a best constant factor involving the β function. An applications, we consider the equivalent form and some particular results.
文摘Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.
基金Supported by the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (gxyqZD2020022)the University Natural Science Research Project of Anhui Province (2022AH040067)+1 种基金the Fundamental Research Funds for the Central Universities (3132023202)National Natural Science Foundation of China (12001080).
文摘Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this paper,we investigate the relative positive center set of planar convex bodies.As an application of the relative positive center,we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.
基金supported by the National Natural Science Foundation of China (90818020,60873206)the Foundation of Innovation Team of Science and Technology of Zhejiang Province of China (2009R50024)
文摘Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the socalled multivariate weighted Bernstein, Nikol＇skii, and Ul＇yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol＇skii-type and Ul＇yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.
文摘A new improvement of Hilbert's inequality for double series can be establishedby means of a strengthened Cauchy's inequality. As application, a quite sharp result onFejer-Riesz's inequality is obtained.
