Kernel Decompositions for Schur Functions on the Polydisk

A certain kernel (sometimes called the Pick kernel) associated to Schur functions on the disk is always positive semi-definite. A generalization of this fact is well-known for Schur functions on the polydisk. In this article, we show that the “Pick kernel” on the polydisk has a great deal of structure beyond being positive semi-definite. It can always be split into two kernels possessing certain shift invariance properties.     

HG凸函数的Hermite-Hadamard型不等式

利用Cauchy-Schwarz不等式、Young不等式和HG凸函数定义,得到几个HG凸函数的Hermite-Hadamard型不等式.     

关于GA-凸函数的若干Hadamard型不等式

利用GA-凸函数的定义及其Hadamard型不等式,得到与重积分有关的GA-凸函数Hadamard型不等式的推广和加细.     

Hermite-Hadamard Type Inequalities for Operator h-preinvex Functions

Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases.     

凸函数的几个Hadamard型不等式

对于凸函数建立了几个新的 Hadamard型不等式 ,比如f ∑nk=1qkak∫A+yA- yg(x) dx ∫A+yA- yf (x) g(x) dx ∑nk=1qkf (ak) ∫A+yA- yg(x) dx和f (pa +qb) p∫ξaf (x) g(x) dx∫ξag(x) dx+q∫bξf (x) g(x) dx∫bξg(x) dx pf (a) +qf (b)等 ,推广了前人所做的工作 .     

调和函数Levin型不等式的注记

针对半空间中的一类调和函数,本文给出了一个广义的Levin型不等式,所得结果推广了张-邓-高的相关结论.     

Weighted Integrals and Bloch Spaces of n-Harmonic Functions on the Polydisc

We study anisotropic mixed norm spaces h(p,q,α) consisting of n-harmonic functions on the unit polydisc of by means of fractional integro-differentiation including small 0 < p < 1 and multi-indices α = (α ₁,...,α _n ) with non-positive α _j  ≤ 0. As an application, two different Bloch spaces of n-harmonic functions are characterized.      

Gaussian Analytic Functions in the Polydisk

We study hyperbolic Gaussian analytic functions in the unit polydisk of \(\mathbb {C}^n\). Following the scheme previously used in the unit ball, we first study the asymptotics of fluctuations of linear statistics as the directional intensities \(L_j\), \(j=1,\dots ,n\) tend to \(\infty \). Then, we estimate the probability of large deviations of such linear statistics and use the estimate to prove a hole theorem. Our proofs are inspired by the methods of M. Sodin and B. Tsirelson for the one-dimensional case, and B. Shiffman and S. Zelditch for the study of the analogous problem for compact Kähler manifolds.     

s-对数凸函数的Hermite-Hadamard型积分不等式

该文定义了"s-对数凸函数"的概念,并给出了可微s-对数凸函数的若干个HermiteHadamard型积分不等式,作为应用给出了平均数的几个不等式.     

Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups

For a Carnot group G,we establish the relationship between extended mean values and r-convexfunctions which is introduced in this paper,which is a class of inequalities of Hadamard type for r-convexfunction on G.     

Inequalities for Cyclic Functions

The nth cyclic function is defined by

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We prove that if k is an integer with 1kn−1, then

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holds for all positive real numbers x with the best possible constantsα=1 and β= 2n-k over n.     

Inequalities for Rational Functions

A new hyperbolic area estimate for the level sets of finite Blaschke products is presented. The following inversion of the usual Sobolev embedding theorem is proved:

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Hereris a rational function of degreenwith poles outside . This estimate implies a new inverse theorem for rational approximation of analytic functions with respect to areaL^pnorm.     

Some Inequalities for Superharmonic Functions on Graphs

An inequality for superharmonic functions on Riemannian manifolds due to S.Y. Cheng and S-T. Yau is adapted to the setting of graphs. A number of corollaries are discussed, including a Harnack inequality for graphs having at most quadratic growth and satisfying a certain connectedness condition.     

Sharp Inequalities for BMO Functions

The purpose of the paper is to study sharp weak-type bounds for functions of bounded mean oscillation. Let 0 p ∞ be a fixed number and let I be an interval contained in R. The author shows that for any φ : I → R and any subset E I of positive measure,For each p, the constant on the right-hand side is the best possible. The proof rests on the explicit evaluation of the associated Bellman function. The result is a complement of the earlier works of Slavin, Vasyunin and Volberg concerning weak-type, L ~p and exponential bounds for the BMO class.     

Weighted Inequalities for Quasi-Monotone Functions

The purpose of this paper is to give characterizations of weightsfor which reverse inequalities of Hölder type for quasi-monotonefunctions are satisfied. Our inequalities with general weightsand with sharp constants complement the results of [2, 8, 9]and [16, 17] for the values of parameters p and q with 1pq<.