用卷积定义的解析函数子类的Fekete-Szeg不等式

本文研究了一个新的解析函数子类Mλ(g,h,u,v,φ)(0≤λ≤1)的系数不等式.利用分析的方法和技巧,得到它精确的Fekete-Szeg不等式及通过分式微分定义的函数类的Fekete-Szeg不等式.所得结果推广了一些作者的相关结果.     

A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS

In this paper we introduce new classes of analytic functions with fixed argument of coefficients defined by subordination. Coefficient estimates, distortion theorems, integral means inequalities, and the radii of convexity and starlikeness are investigated. Convolution properties are also pointed out.     

The Starlikeness of Analytic Functions of Koebe Type with Complex Order

For α 0, λ 0 and β,η∈R, we consider the M(α,λ)_b of normalized analyticα—λ convex functions defined in the open unit disc U. In this paper we investigate the class M(α, λ,β,η)_b,with f_b := z/(1-z~n)~b being Koebe type. By making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class M(α, λ, β, η)_b of n-fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in earlier works are also indicated.     

Orlicz空间非负下鞅微分从属不等式

本文在Orlicz空间中推广了Burkholder关于非负下鞅与其微分从属的不等式.     

用广义拟Hadamard卷积定义的广义积分算子的封闭性质

首先利用广义拟-Hadamard卷积引入一个广义积分算子;其次,应用两个经典不等式和系数不等式研究广义积分算子及其特殊殊算子在某些非标准化广义解析函数类上的封闭性质.     

Hypercontractivity, Nash inequalities and subordination for classes of nonlinear semigroups

A suitable notion of hypercontractivity for a nonlinear semigroup {T _t } is shown to imply Nash-type inequalities for its generator H, provided a subhomogeneity property holds for the energy functional (u,Hu). We use this fact to prove that, for semigroups generated by operators of p-Laplacian-type, hypercontractivity implies ultracontractivity. Then we introduce the notion of subordinated nonlinear semigroups when the corresponding Bernstein function is f(x)=x ^α , and write an explicit formula for the associated generator. It is shown that hypercontractivity still holds for the subordinated semigroup and, hence, that Nash-type inequalities hold as well for the subordinated generator.     

Capacitary Upper Estimates for Symmetric Dirichlet Forms

Upper estimates for capacities are studied for symmetric Dirichlet forms which do not necessarily admit intrinsic metric. Firstly, a general method of obtaining a sharp estimate from upper estimates for cut-off functions are provided in the local and non-local cases. Secondly, a capacitary upper estimate is established for the skew product of two symmetric Dirichlet forms for which suitable capacitary estimates are given. Several examples of capacitary upper inequalities in the local and non-local cases are also given. Especially, an upper estimate for the capacity is proved for the symmetric Dirichlet form associated to the Markov process subordinated (in the Bochner sense) to the skew product of two one-dimensional Brownian motions with respect to the local time of the first Brownian motion at the origin. This estimate is used in the recent work by the present author to establish the sharp criteria for recurrence and transience of the above-mentioned process.     

Libera transform of functions with bounded turning

Conditions are determined for the starlikeness of the Libera transform of functions of bounded turning. In addition, several other differential subordinations and differential inequalities are considered.     

A pointwise inequality for fractional laplacians

The fractional laplacian is an operator appearing in several evolution models where diffusion coming from a Lévy process is present but also in the analysis of fluid interphases. We provide an extension of a pointwise inequality that plays a rôle in their study. We begin recalling two scenarios where it has been used. After stating the results, for fractional Laplace–Beltrami and Dirichlet–Neumann operators, we provide a sketch of their proofs, unravelling the underlying principle to such inequalities.     

星像与强星像的某些充分条件(英文)

本文研究了与某些新的函数表达式相关的一些微分不等式及一阶微分从属关系的问题.利用微分从属的方法,获得了一些新的函数星像性与强星像性的充分条件,推广和改进了已有的一些结果.     

Functional inequalities for the Wright functions

In this paper, our aim is to show some mean value inequalities for the Wright function, such as Turán-type inequalities, Lazarevi?-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for sections of series of Wright functions, the result is also closely connected with Turán-type inequalities. In the end of the paper, we present some other inequalities for the Wright function.     

Functional inequalities for transient birth-death processes and their applications

We give a new diagram about uniform decay, empty essential spectrum and various functional inequalities, including Poincaré inequalities, super- and weak-Poincaré inequalities, for transient birth-death processes. This diagram is completely opposite to that in ergodic situation, and substantially points out the difference between transient birth-death processes and recurrent ones. The criterion for the empty essential spectrum is achieved. Some matching sufficient and necessary conditions for weak-Poincaré inequalities and super-Poincaré inequalities are also presented.     

Convex and alpha-prestarlike subordination chains

In this paper we consider convex subordination chains (c.s.c.) and alpha-prestarlike subordination chains (α-p.s.c.) over (0,1] on the unit disc in the complex plane. We obtain sufficient conditions for a mapping f(z,t) to be an α-p.s.c. over (0,1], which generalize a well-known result of Ruscheweyh [St. Ruscheweyh, Convolutions in Geometric Function Theory, Les Presses de l'Université de Montreal, 1982]. We also obtain sufficient conditions for injectivity for nonanalytic mappings on the unit disc, and give certain examples of α-c.s.c. over (0,1] on the unit disc.     

Mass transportation proofs of free functional inequalities, and free Poincaré inequalities

This work is devoted to direct mass transportation proofs of families of functional inequalities in the context of one-dimensional free probability, avoiding random matrix approximation. The inequalities include the free form of the transportation, Log-Sobolev, HWI interpolation and Brunn-Minkowski inequalities for strictly convex potentials. Sharp constants and some extended versions are put forward. The paper also addresses two versions of free Poincaré inequalities and their interpretation in terms of spectral properties of Jacobi operators. The last part establishes the corresponding inequalities for measures on R₊ with the reference example of the Marcenko-Pastur distribution.     

Mixing mixed-integer inequalities

Mixed-integer rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixed-integer programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities.?Given a mixed-integer region S and a collection of valid “base” mixed-integer inequalities, we develop a procedure for generating new valid inequalities for S. The starting point of our procedure is to consider the MIR inequalities related with the base inequalities. For any subset of these MIR inequalities, we generate two new inequalities by combining or “mixing” them. We show that the new inequalities are strong in the sense that they fully describe the convex hull of a special mixed-integer region associated with the base inequalities.?We discuss how the mixing procedure can be used to obtain new classes of strong valid inequalities for various mixed-integer programming problems. In particular, we present examples for production planning, capacitated facility location, capacitated network design, and multiple knapsack problems. We also present preliminary computational results using the mixing procedure to tighten the formulation of some difficult integer programs. Finally we study some extensions of this mixing procedure. Received: April 1998 / Accepted: January 2001?Published online April 12, 2001     

Poincaré and Sobolev Inequalities for Vector Fields Satisfying Hrmander's Condition in Variable Exponent Sobolev Spaces

In this paper,we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces.The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type.We obtain the first order Poincare inequalities for vector fields satisfying Hrmander's condition in variable non-isotropic Sobolev spaces.We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups.Moreover,we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups.These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p(x)-subLaplacian.Our results are only stated and proved for vector fields satisfying Hrmander's condition,but they also hold for Grushin vector fields as well with obvious modifications.     

Capacitary Criteria for Poincaré-Type Inequalities

The Poincaré-type inequality is a unification of various inequalities including the F-Sobolev inequalities, Sobolev-type inequalities, logarithmic Sobolev inequalities, and so on. The aim of this paper is to deduce some unified upper and lower bounds of the optimal constants in Poincaré-type inequalities for a large class of normed linear (Banach, Orlicz) spaces in terms of capacity. The lower and upper bounds differ only by a multiplicative constant, and so the capacitary criteria for the inequalities are also established. Both the transient and the ergodic cases are treated. Besides, the explicit lower and upper estimates in dimension one are computed. Mathematics Subject Classifications (2000) 60J55, 31C25, 60J35, 47D07.Research supported in part NSFC (No. 10121101) and 973 Project.     

Certain family of integral operators preserving subordination and superordination

We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also derived, and the results generalize some recently ones.