We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interactio...We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.展开更多
Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality...Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented.展开更多
In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient an...In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from Lp(G, xα) to Lq(G, xβ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < +∞, norms of the operators H and H* are obtained.展开更多
Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be poin...Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be pointed out that we con- sider whole ranges of p and q, i.e., 0 〈 p ≤∞ and 0 〈 q ≤∞.展开更多
In this paper, by introducting a weight coefficient of the form: π/sin(π/r)-1/10(2n+1)1+1/r (r＞1, n∈N0), Hardy-Hilbert's inequality is refined. As its applications, an equivalent Hard y-Hilbert's typ...In this paper, by introducting a weight coefficient of the form: π/sin(π/r)-1/10(2n+1)1+1/r (r＞1, n∈N0), Hardy-Hilbert's inequality is refined. As its applications, an equivalent Hard y-Hilbert's type inequality and its strengthened form are given, and Hardy-Li ttlewood's inequality is generalized and improved.展开更多
The Hardy-Littlewood-PSlya （HLP） inequality [1] states that if a ∈ lp, b ∈ 1q and In this article, we prove the HLP inequality in the case where A = 1,p = q = 2 with a logarithm correction, as conjectured by Ding ...The Hardy-Littlewood-PSlya （HLP） inequality [1] states that if a ∈ lp, b ∈ 1q and In this article, we prove the HLP inequality in the case where A = 1,p = q = 2 with a logarithm correction, as conjectured by Ding [2]：In addition, we derive an accurate estimate for the best constant for this inequality.展开更多
In this paper, by introducing three parameters a, b and λ, we give some new generalizations of Hardy-Hilbert’s integral inequality. As applications, we con-sider its equivalent form and some particular results.
We give an analytic quantitative relation between Hardy＇s non-locality and Bell operator. We find that Hardy＇s non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy＇s...We give an analytic quantitative relation between Hardy＇s non-locality and Bell operator. We find that Hardy＇s non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy＇s non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy＇s non- locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the CabeUo＇s argument of Hardy＇s non-locality （a generalization of Hardy＇s argument） and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy＇s non-locality under the constraint of information causality with the aid of the above derived relation between Hardy＇s non-locality and Bell operator.展开更多
In this paper we shall extend Hardy＇s inequality associated with Fourier trans- form to the strip n（2-p） ≤σ〈 n＋p（N＋ 1） where N = [n（1/p- 1）], the greatest integer not exceeding n（1/p - 1）.
In this paper, by introducing the norm ｜｜x｜｜ （x ∈ Rn）, a multiple Hardy- Hilbert＇s integral inequality with the best constant factor and it＇s equivalent form are given.
In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the...In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the gradient operator defined by ▽_γ =(▽_x,|x|~γ▽_y) and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽_γ.展开更多
Inequalities are essential in the study of Mathematics and are useful tools in the theory of analysis. They have been playing a critical role in the study of the existence and uniqueness properties of solutions of ini...Inequalities are essential in the study of Mathematics and are useful tools in the theory of analysis. They have been playing a critical role in the study of the existence and uniqueness properties of solutions of initial and boundary value problems for differential equations as well as difference equations with their bounds. In this paper, we obtain new integral inequalities mainly by using some known inequalities. Various generalizations of Hardy's inequality are special cases of the results therein.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, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as ...In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.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
文摘We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.
文摘Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented.
基金supported by National Natural Science Foundation of China (Grant Nos.11071250 and 10931001)
文摘In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from Lp(G, xα) to Lq(G, xβ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < +∞, norms of the operators H and H* are obtained.
基金supported in part by National Natural Foundation of China (Grant Nos. 11071250 and 11271162)
文摘Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be pointed out that we con- sider whole ranges of p and q, i.e., 0 〈 p ≤∞ and 0 〈 q ≤∞.
文摘In this paper, by introducting a weight coefficient of the form: π/sin(π/r)-1/10(2n+1)1+1/r (r＞1, n∈N0), Hardy-Hilbert's inequality is refined. As its applications, an equivalent Hard y-Hilbert's type inequality and its strengthened form are given, and Hardy-Li ttlewood's inequality is generalized and improved.
基金supported by the NSF grants DMS-0908097 and EAR-0934647
文摘The Hardy-Littlewood-PSlya （HLP） inequality [1] states that if a ∈ lp, b ∈ 1q and In this article, we prove the HLP inequality in the case where A = 1,p = q = 2 with a logarithm correction, as conjectured by Ding [2]：In addition, we derive an accurate estimate for the best constant for this inequality.
基金Foundation item:The NSF (0177) of Guangdong Institutions of Higher Learning,College and University
文摘In this paper, by introducing three parameters a, b and λ, we give some new generalizations of Hardy-Hilbert’s integral inequality. As applications, we con-sider its equivalent form and some particular results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10947142 and 11005031)
文摘We give an analytic quantitative relation between Hardy＇s non-locality and Bell operator. We find that Hardy＇s non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy＇s non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy＇s non- locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the CabeUo＇s argument of Hardy＇s non-locality （a generalization of Hardy＇s argument） and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy＇s non-locality under the constraint of information causality with the aid of the above derived relation between Hardy＇s non-locality and Bell operator.
文摘In this paper we shall extend Hardy＇s inequality associated with Fourier trans- form to the strip n（2-p） ≤σ〈 n＋p（N＋ 1） where N = [n（1/p- 1）], the greatest integer not exceeding n（1/p - 1）.
文摘In this paper, by introducing the norm ｜｜x｜｜ （x ∈ Rn）, a multiple Hardy- Hilbert＇s integral inequality with the best constant factor and it＇s equivalent form are given.
基金Foundation item： Supported by the Natural Science Foundation of Zhejiang Province（Y6090359, Y6090383） Supported by the Department of Education of Zhejiang Province（Z200803357）
文摘In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_(p,γ,α)u = ▽_γ·(|▽_γu|^(p-2)ρ~α▽_γu) on R^(m+n )with singularity at the origin,where ▽_γ is the gradient operator defined by ▽_γ =(▽_x,|x|~γ▽_y) and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽_γ.
文摘Inequalities are essential in the study of Mathematics and are useful tools in the theory of analysis. They have been playing a critical role in the study of the existence and uniqueness properties of solutions of initial and boundary value problems for differential equations as well as difference equations with their bounds. In this paper, we obtain new integral inequalities mainly by using some known inequalities. Various generalizations of Hardy's inequality are special cases of the results therein.
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, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.
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.
