上半空间中一类次调和函数的增长估计

本文证明了n-维(n≥2)Euclidean空间的上半空间中Poisson积分在无穷远点处的增长性质.同时将这个性质推广到次调和函数中去,其概括了解析函数和调和函数的增长性质.     

锥中一类调和函数的增长估计

给出了锥中一类调和函数在无穷远点处的增长估计,推广了Siegel和Talvila,张和邓在半空间的相关结果.     

半空间中一类推广的Poisson积分的增长性质

本文研究了推广的Poisson积分的增长性问题.利用复平面中经典的Hayman定理及其证明方法,通过修改上半空间中的Poisson积分,获得了上半空间中一类位势在无穷远点的增长性质,推广了Hayman定理在高维空间的结果.     

无限管状区域上次调和函数的边界性质

作者刻画了定义在无限管状区域中次调和函数的边界性质.通过证明一类新型的Phragmen-Lindelof定理,不仅得到了与之相关最大模极限的存在性定理,而且还得到了其具体的表达式.     

半平面中调和函数的积分表示

本文对于半平面中的调和函数u(z),证明了正部u (z)满足某些限制增长条件,用半平面边界上的积分表示,它的负部u-(z)也被类似的增长条件所控制.得到了半平面中负的调和函数的经典结果.     

半平面中调和函数的积分表示和估计

对于半平面中的调和函数,在本文中证明了如果它的正部满足某些限制增长条件,则它可以用半平面边界上的积分表示出来并且它的绝对值也满足类似的增长条件,这一结果改进了在半平面中调和函数的某些经典结果.     

黎曼曲面上的φ-调和函数和φ-次调和函数

(M,g)是黎曼曲面,该文给出了M上函数的φ-Dirichlet积分的定义,并在此基础上 得到了一个关于具有有限的φ-Dirichlet积分的φ-次调和函数的有界性定理．     

半平面中调和函数的积分表示

In this article, we consider the integral representation of harmonic functions. Using a property of the modified Poisson kernel in a half plane, we prove that a harmonic function u（z） in a half plane with its positive part u^＋（z） = max{u（z）, 0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.     

修改的Poisson核和调和函数的积分表示

在本文中,对于半平面中的调和函数u(z),利用半平面中修改的Poisson核,证明了如果它的正部u~ (z)=max{u(z),0}满足某些限制增长条件,则它可以用半平面边界上的积分表示出来,并且它的负部u~-(z)=max{-u(z),0}也被类似的增长条件所控制,这一结果改进了在半平面中调和函数的某些经典结果。     

半空间中一类调和函数的例外集

利用Whitney方体的相关性质, 给出了一类调和函数在半空间中无穷远点处的增长估计, 且刻画了其 例外集的几何性质. 本文推广了张艳慧和邓冠铁在半空间中的相关结果.     

Subharmonic Functions in the Unit Ball

For functions u subharmonic in the unit ball B_N of , this paper compares the growth of the repartition function of their Riesz measure μ with the growth of u near the boundary of B_N. Cases under study are: and , with A, B, γ positive constants and if N=2 or if N≥ 3. This paper contains several integral results, as for instance: when ∫_BN u⁺(x)[-ω^′(|x|²)]dx < +∞ for some positive decreasing C¹ function ω, it is proved that .     

Subharmonic Functions of Order Less than One

We study suhharmonic functions u in R^N (N3) of order at most one, growing so slowly that for some function , with M(u,r)=max_|x|=ru(x). We obtain minorisations for negative values of u(x) and estimations of the difference u(y)–u(x) for x and y on a same sphere. Mathematics Subject Classifications (2000) 31B05, 31B10; secondary: 26A12, 26D15.     

一类一阶Hamilton系统的次调和解

运用临界点理论中的极小极大方法得到一类一阶Hamilton系统的次调和解的存在性定理.     

一类积分函数的SC^1性质

研究一类积分函数的半光滑性和SC^1性质,所得结果在求解随机线性互补问题的Newton算法的收敛性分析中起关键作用.     

一类积分函数的SC~1性质

研究一类积分函数的半光滑性和SC1性质,所得结果在求解随机线性互补问题的Newton算法的收敛性分析中起关键作用.     

A Liouville-Type Theorem for Strongly Subharmonic Functions on Complete Non-compact Riemannian Manifolds and Some Applications

We prove that if Mis a complete non-compact Riemannian manifold and ₁(M)=0, then any C ²solution of uk> 0 is unbounded. We apply this result to obtain an estimate for the size of the image set of some types of maps between Riemannian manifolds.     

Classes of Quasi-nearly Subharmonic Functions

It is well known and important that if u ≥ 0 is subharmonic on a domain Ω in ℝ ⁿ and p > 0, then there is a constant C(n,p) ≥ 1 such that for each open ball B(x,r) ⊂ Ω. The definition of a relatively new function class, quasi-nearly subharmonic functions, is based on such a generalized mean value inequality. It is pointed out that the obtained function class is natural. It has important and interesting properties and, at the same time, it is large: In addition to nonnegative subharmonic functions, it includes, among others, Hervé’s nearly subharmonic functions, functions satisfying certain natural growth conditions, especially certain eigenfunctions, polyharmonic functions and generalizations of convex functions. Further, some of the basic properties of quasi-nearly subharmonic functions are stated in a unified form. Moreover, a characterization of quasi-nearly subharmonic functions with the aid of the quasihyperbolic metric and two weighted boundary limit results are given.      

Sharp Growth Estimates for Modified Poisson Integrals in a Half Space

For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in Rⁿ. Pointwise growth estimates for these integrals are given and the estimates are proved sharp in a strong sense. For decaying data, a new type of modified Poisson integral is introduced and used to develop asymptotic expansions for solutions of these half space problems.