凸域的外平行集的包含测度

本文研究了凸域内定长线段的包含测度问题,利用广义支持函数和限弦函数,得到了一类特殊凸域的包含测度.     

On the zeros of functions in Bergman spaces and in some other related classes of functions

A well-known theorem of H.S. Shapiro and A.L. Shields implies that if f?0 is a function which belongs to the Bergman space Ap (0<p<∞) and {zk} is a sequence of zeros of f which is contained in a Stolz angle, then {zk} satisfies the Blaschke condition. In this paper we improve this result. We consider a large class of regions contained in the unit disc D which touch ∂D at a point ξ tangentially and we prove that the mentioned result remains true if we substitute a Stolz angle by any of these regions of tangential approach.     

Integral Representations in Linearly Convex Polyhedra

We introduce the notion of mixed Levian (Levi determinant) of a system of k Hermitian and k linear forms. In terms of these Levians we obtain an integral formula for holomorphic functions in linearly convex polyhedra.Original Russian Text Copyright © 2005 Krivokolesko V. P. and Tsikh A. K.The first author was supported by a grant of the President of the Russian Federation and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1212.2003.1); the second author was supported by the Ministry for Education of the Russian Federation (St. Petersburg, Grant 02-1-138).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 579–593, May–June, 2005.     

Vector-valued weak martingale Hardy spaces and atomic decompositions

Some atomic decomposition theorems are proved in vector-valued weak martingale Hardy spaces w _p Σ_α(X), w _p Q _α(X) and wD _α(X). As applications of atomic decompositions, a sufficient condition for sublinear operators defined on some vector-valued weak martingale Hardy spaces to be bounded is given. In particular, some weak versions of martingale inequalities for the operators f*, S ^(p)(f) and σ^(p)(f) are obtained. This research was supported by the National Science Foundation of China (No. 10371093).     

复Swift-Hohenberg方程在一些Banach空间内的指数吸引子

本文研究了N-维(N≤3)复Swift-Hohenberg方程在一些Banach空间x~α中解的渐近行为.运用Cholewa等人的技巧,证明了整体解的存在性以及整体吸引子A的存在性.最后,作为本文的另—个主要结果,证明了指数吸引子M的存在性,从而得到A有有限的分形维数.由于应用于Hilbert空间中所谓的挤压性质在我们的框架下不能成立,为了构造M,没有应用Hilbert空间中的标准的方法,而是应用Efendiev,Miranville,和Zelik最近的结果.     

Normal fields of functionals and optimal measurable sections

We study some classes of extended real-valued functions on measurable fields of metric spaces and give sufficient conditions for the existence of optimal measurable sections.The author is grateful to A. Kucia for Lemma 3.3, Theorem 3.1 (i), and helpful discussions.     

THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES

In this paper we show that in error estimates, the condition number k(T) of any in-vertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Ba-nach theorem and other related results.     

On a parabolic equation in a triangular domain

We prove the optimal regularity, in Sobolev spaces, of the solution of a parabolic equation set in a triangular domain T. The right-hand term of the equation is taken in Lebesgue space L^p(T). The method of operators sums in the non-commutative case is referred to.     

Banach空间闭子集上微分方程解的整体存在唯一性定理

本文利用比较方法和Kuratowski非紧致测度研究Banach空间闭子集上微分方程解的整体存在唯一性,得出了一个一般性判别准则.作为特例,本文的结果包含了文[4]中的主要定理.     

Banach空间的弱*序列紧性

本文研究了Ｂａｎａｃｈ空间的弱序列紧性．Ｂａｎａｃｈ空间Ｘ称为有（ｗ）性质，如果Ｘ（Ｘ的共轭空间）的每个有界序列有弱收敛子列．我们证明了，如果Ｂａｎａｃｈ空间Ｘ有（ｗ）性质，那么ｌｐ（Ｘ）（１≤ｐ＜＋∞）与ｃ０（Ｘ）也有（ｗ）性质．