一个对偶的Hardy-Hilbert不等式及其推广

本文给出一个对偶的具有最佳常数因子的Hardy-Hilbert不等式,它是Hilbert不等式的具有(p,q)-参数形式的新推广,还考虑了它的更为推广的单参数形式及一个等价不等式。     

Two new forms of half-discrete Hilbert inequality

In this paper, we introduce two new forms of the half-discrete Hilbert inequality. The first form is a sharper form of the half-discrete Hilbert inequality and is related to Hardy inequality. In the second one, we give a differential form of this inequality.     

一个关于非负矩阵的不等式

证明:若(xij)是一个元素不全为零的m×n非负矩阵,则当0相似文献   

Functional Inequalities for the Decay of Sub-Markov Semigroups

A general functional inequality is introduced to describe various decays of semigroups. Our main result generalizes the classical one on the equivalence of the L ²-exponential decay of a sub-Markov semigroup and the Poincaré inequality for the associated Dirichlet form. Conditions for the general inequality to hold are presented. The corresponding isoperimetric inequality is studied in the context of diffusion and jump processes. In particular, Cheeger's inequality for the principal eigenvalue is generalized. Moreover, our results are illustrated by examples of diffusion and jump processes.     

球面上的次临界最佳Sobolev不等式

本文在球面SN上建立了一类最佳Sobolev不等式:‖f‖2Lq(SN)≤(q-2)Γ(N-d)2+1/dΓ(N+d/2))(∫SNf(ξ)Adf(ξ)dξ-Γ(N+d/2)Γ/(N-d/2)∫SN |f丨2dξ)+∫SN丨f丨2dξ,其中Ad(0＜d＜N)是SN上的高阶保形算子,dξ是SN的归一化曲面测度,2≤q＜2...     

Analysis on free Riemannian path spaces

The gradient operator is defined on the free path space with reference measure Pμ, the law of the Brownian motion on the base manifold with initial distribution μ, where μ has strictly positive density w.r.t. the volume measure. The formula of integration by parts is established for the underlying directional derivatives, which implies the closability of the gradient operator so that it induces a conservative Dirichlet form on the free path space. The log-Sobolev inequality for this Dirichlet form is established and, consequently, the transportation cost inequality is obtained for the associated intrinsic distance.     

关于一个推广的Hardy-Hilbert不等式

本文引入参数λ,给出一个具有最佳常数因子的推广的Ｈａｒｄｙ－Ｈｉｌｂｅｒｔ不等式,并考虑了它的等价形式及对应的积分不等式．     

A Remark on the Hörmander Inequality

A sufficient condition is given in order to ensure the Hörmander inequality for a (formally) self-adjoint transversally elliptic pseudodifferential operator P in the case of the symplectic form changing rank on the characteristic manifold.     

Functional inequality on path space over a non-compact Riemannian manifold

We prove the existence of the O-U Dirichlet form and the damped O-U Dirichlet form on path space over a general non-compact Riemannian manifold which is complete and stochastically complete. We show a weighted log-Sobolev inequality for the O-U Dirichlet form and the (standard) log-Sobolev inequality for the damped O-U Dirichlet form. In particular, the Poincaré inequality (and the super Poincaré inequality) can be established for the O-U Dirichlet form on path space over a class of Riemannian manifolds with unbounded Ricci curvatures. Moreover, we construct a large class of quasi-regular local Dirichlet forms with unbounded random diffusion coefficients on path space over a general non-compact manifold.     

On new extensions of Hilbert's inequality

By introducing three parameters A, B and α, and estimating the weight coefficient, we give a new extension of Hilbert's inequality with a best constant factor involving the β function. As applications, we consider the equivalent form and some particular results. This revised version was published online in June 2006 with corrections to the Cover Date.     

HARDY-HILBERT不等式一个新的推广与改进

给出了如下形式的权系数ω(q,n)∶=∑1m +nnm1/ q<πsin(π/ p) -1abn1/ q +n -1 / qq >1 ,1P +1q =1 ,n∈N ,a >0 ,b >0 ,0 相似文献   

一个新的Hilbert型不等式及其等价形式

引入参数和权系数,通过对权系数估算,给出一个新的核为-2齐次的Hilbert型不等式及其等价形式,并应用复分析方法,求出其最佳的常数因子,同时给出了其逆向不等式.     

一个核含无理式的Hilbert型不等式

应用权系数方法,给出一个带有最佳常数因子且核含有无理式的Hilbert型不等式,同时给出其逆向不等式及其等价形式.     

Parabolic Harnack inequality for divergence form second order differential operators

Old and recent results concerning Harnack inequalities for divergence form operators are reviewed. In particular, the characterization of the parabolic Harnack principle by simple geometric properties -Poincaré inequality and doubling property- is discussed at length. It is shown that these two properties suffice to apply Moser's iterative technique.     

Global existence of small amplitude solution for the generalized IMBq equation

In this paper, we reconsider the problem discussed in [G.W. Chen, S.B. Wang, Small amplitude solutions of the generalized IMBq equation, J. Math. Anal. Appl. 274 (2002) 846-866]. The proof of global existence presented in [G.W. Chen, S.B. Wang, Small amplitude solutions of the generalized IMBq equation, J. Math. Anal. Appl. 274 (2002) 846-866] is very simple in form, but it is a pity that the authors overlooked the bad behavior of low frequency part of B(t)ψ which causes trouble in L^∞ and Hs estimates. In this paper, we will give out a new proof of the global existence under an additional condition on the initial data.     

Hardy's Inequality for Dirichlet Forms

We prove an abstract form of Hardy's L² inequality, in which the Dirichlet integral is replaced by the Dirichlet form of a general symmetric Markov process. A number of examples are provided.     

Integrability of optimal mappings

In this paper, we study the integrability of optimal mappings T taking a probability measure μ to another measure g · μ. We assume that T minimizes the cost function c and μ satisfies some special inequalities related to c (the infimum-convolution inequality or the logarithmic c-Sobolev inequality). The results obtained are applied to the analysis of measures of the form exp(?|x|^α).     

On a continuous form of Hölder inequality

A continuous form of Hölder inequality is considered here extending some known results.     

A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface

In this paper, a sharp form of the Moser-Trudinger inequality is established on a compact Riemannian surface via the method of blow-up analysis, and the existence of an extremal function for such an inequality is proved.

     

Symplectically hyperbolic manifolds

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms. The main results are:

• If a symplectic form represents a bounded cohomology class then it is hyperbolic.

• The symplectic hyperbolicity is equivalent to a certain isoperimetric inequality.

• The fundamental group of symplectically hyperbolic manifold is non-amenable.

We also construct hyperbolic symplectic forms on certain bundles and Lefschetz fibrations, discuss the dependence of the symplectic hyperbolicity on the fundamental group and discuss some properties of the group of symplectic diffeomorphisms of a symplectically hyperbolic manifold.