广义分数次积分算子在齐次加权Morrey-Herz空间上的有界性

本文研究了广义分数次积分算子在齐次加权Morrey-Herz空间上的有界性.利用对函数进行环形分解技术和算子截断的方法,获得了广义分数次积分算子L~(-β/2)(f)从MK_(p,q1)~(α,λ)(ω1,ω_2~(q1))空间到MK_(p,q2)~(α,λ)(ω_1,ω_2~(q2))空间是有界的,从而将分数次积分算子在齐次加权Morrey-Herz空间上的有界性推广到广义分数次积分算子.     

关于L1空间多项式导数的估计

本义在加权Ｌ₁空间中对正导数多项式建立了精确的Ｂｅｒｎｓｔｃｉｎ型不等式．     

在险值与Lp-空间上的连续一致风险度量

本文研究了在险值和L^p-空间上的连续一致风险度量之间的关系.利用凸集分离定理和截尾逼近方法,获得了在险值可以用L^p-空间上的连续一致风险度量表示的结果,并且得到了L^p-空间上的表示定理的一种新的证明方法.它们分别是文献[2]的相关结论从L^∞-空间到L^p-空间上的推广和对Inoue^[4]做的一些补充证明.     

含临界指数p-Kirchhoff型方程的非平凡解

本文研究了一类含临界指数的p-Kirchhoff型方程.利用变分方法与集中紧性原理,通过证明对应的能量泛函满足局部的(PS)_c条件,得到了这类方程非平凡解的存在性,推广了关于Kirchhoff型方程的相关结果.     

F_2+vF_2上的循环码

本文研究了环F_2+vF_2上的循环码.利用标准形生成元集刻画了环F_2+vF_2上的循环码的代数结构,证明了环F_2+vF_2上的每一个非零的循环码均有唯一的标准形生成元集,进而得到了每一个循环码均是由一个多项式生成的.     

态R_0代数

本文研究了R_0代数上有关态算子的问题.利用MV-代数上内态的引入方法引入了态算子,定义了态R_0代数,它是R_0代数的一般化.给出了一些非平凡态R_0代数的例子并讨论了态R_0代数的一些基本性质.在此基础上给出了态滤子和态局部R_0代数的概念,并利用态滤子刻画了态局部R_0代数.推广了局部R_0代数的相关理论.     

非自治p(t)-拉普拉斯系统周期解的存在性

本文研究一类非自治p(t)-Laplace系统.利用鞍点定理和极小作用原理,获得了周期解存在的充分条件,推广和改进了文献[8]中的结果.     

变分不等式问题的解的存在性

对一般凸集约束下的变分不等式问题提出了一个新的例外簇概念.基于此概念,给出了变分不等式问题解存在的一个充分条件,此条件弱于许多已知的关于变分不等式问题的解的存在性条件.对于伪单调变分不等式问题,它是解存在的充要条件.对于P₀非线性互补问题,利用例外簇的概念,给出了其解存在的充分条件.     

可除阿贝尔p-群的自同构群

主要探讨了秩大于或者等于p-1的可除阿贝尔p-群的p-自同构群,并且得到这些p-自同构如何作用在该可除阿贝尔p-群上.这些结论有助于进一步理解 ?ernikov p-群的结构.     

非交换Hp空间理论的若干进展——纪念李国平院士吴新谋教授诞辰100周年

该文分两部分综述非交换H_p 空间理论的研究背景、发展线路以及某些最新进展.第一部分介绍非交换Hardy 空间理论, 包括有限次对角代数的基本性质 (如唯一正规态开拓性质、分解性质、对数模性、不变子空间性质等),Szeg\"{o} 与Riesz 型分解定理和H¹-BMO 对偶定理等. 第二部分综述非交换 H_p鞅空间理论, 主要介绍各种非交换鞅不等式以及作者与合作者在非交换Hardy 鞅空间原子分解方面获得的最新结果. 该文还给出了非交换H_p空间理论有待解决的一些问题 和潜在的发展方向.     

The L p -curvature images of convex bodies and L p -projection bodies

Associated with the L _p -curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L _p -projection bodies are established. As a natural extension of a result due to Lutwak, an L _p -type affine isoperimetric inequality, whose special cases are L _p -Busemann-Petty centroid inequality and L _p -affine projection inequality, respectively, is established. Some L _p -mixed volume inequalities involving L _p -projection bodies are also established.     

<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-mixed intersection bodies

In this paper the author first introduce a new concept of L _p -dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L _p intersection body to L _p -mixed intersection body. Inequalities for L _p -dual mixed volumes of L _p -mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities. This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

Some complete metrics on spaces of fuzzy subsets

The classes of the L_p,∞- and L_p-metrics play an important role to develop a probability theory in fuzzy sample spaces. All of these metrics are known to be separable, but not complete. The classes are closely related as for each L_p,∞-metric there exists some L_p-metric which induces the same topology. This paper deals with the completion of the L_p,∞- and L_p-metrics. We can also show that the relationship between the classes of L_p,∞- and L_p-metrics still holds for the obtained respective classes of their completions.     

Connections between stability and asymptotic stability of nonlinear switched systems

Here are considered nonlinear switched systems in which the switching occurs among a class of subsystems that are characterized by input–output properties stated in terms of L_p spaces of signals. The relationships between the L_p stability of each subsystem and the internal stability of the switched system are studied. In particular, conditions on the dwell time of the switching signals that guarantee the asymptotic stability of the overall system are provided. The connections among these conditions and the L_p input–output properties of the subsystems are investigated.     

<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> discrepancy of generalized two-dimensional Hammersley point sets

We determine the L _p discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the L _p discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound on L _p discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the Hammersley point set and show that there always exist permutations such that the L _p discrepancy of the generalized Hammersley point set is of best possible order. For the L ₂ discrepancy such permutations are given explicitly. F.P. is supported by the Austrian Science Foundation (FWF), Project S9609, that is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory”.     

Lp-Approximable Sequences of Vectors and Limit Distribution of Quadratic Forms of Random Variables

The properties of L₂-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are “two-wing” averages of martingale differences. The results constitute the first significant advancement in the theory of L₂-approximable sequences since 1976 when Moussatat introduced a narrower notion of L₂-generated sequences. The method relies on a study of certain linear operators in the spaces L_p and l_p. A criterion of L_p-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.     

Point sets with low <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-discrepancy

In this paper we study the L _p -discrepancy of digitally shifted Hammersley point sets. While it is known that the (unshifted) Hammersley point set (which is also known as Roth net) with N points has L _p -discrepancy (p an integer) of order (log N)/N, we show that there always exists a shift such that the digitally shifted Hammersley point set has L _p -discrepancy (p an even integer) of order which is best possible by a result of W. Schmidt. Further we concentrate on the case p = 2. We give very tight lower and upper bounds for the L ₂-discrepancy of digitally shifted Hammersley point sets which show that the value of the L ₂-discrepancy of such a point set mostly depends on the number of zero coordinates of the shift and not so much on the position of these. This work is supported by the Austrian Research Fund (FWF), Project P17022-N12 and Project S8305.     

Besov spaces andK-functionals inL p, 0<p<1*

We investigate Besov spaces and their connection with trigonometric polynomial approximation inL _p[−π,π], algebraic polynomial approximation inL _p[−1,1], algebraic polynomial approximation inL _p(S), and entire function of exponential type approximation inL _p(R), and characterizeK-functionals for certain pairs of function spaces including (L _p[−π,π],B _s ^a(L _p[−π,π])), (L _p(R),_s ^a(L_p(R))), , and , where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r. This project is supported by the National Science Foundation of China.     

An analogue of Montel's theorem for some classes of rational functions

For sequences of rational functions, analytic in some domain, a theorem of Montel's type is proved. As an application, sequences of rational functions of the best L _p -approximation with an unbounded number of finite poles are considered.     

Estimates for the L 2-Projection onto Continuous Finite Element Spaces in a Weighted L p -Norm

We consider the orthogonal L₂-projection P onto continuous finite element spaces. We prove estimates for P in a weighted L_p-norm and use these to prove corresponding approximation properties. AMS subject classification (2000) 65N60, 35K85