关于多元函数最佳逼近精确阶的Timan问题

关于找一个充分必要条件使Ω^k(f,1/σ)L_p(Rⁿ)=O(A_σ(f)L_p(Rⁿ)),σ→∞,成立的Timan问题被解决.这个条件是Q^k(f,δ)L_p(Rⁿ)=O(Ω^k+1(f,δ)L_p(Rⁿ)),δ→0.     

相对化概率算法类与非确定算法类的强分离

本文提出并讨论了多项式时间概率型算法复杂度语言类与指数时间非确定型算法复杂度语言类的强分离(即带禁集证据的分离)问题,获得并证明了存在一个递归Oracle集A使得在多项式时间有界错误概率复杂度语言类BPP^A中存在NEXT_k^A禁集,这里NEXT_k^A=∪NTIME^A(2^_cnk)表示计算时间限界于O(2^_nk)的指数时间非确定型算法所接受的语言类;我们指出,Oracle集A可以一致地对k构成并列举熟知的语言类P,NP,U,R,BPP,PP,∑₂^p,∏₂^p,Δ₂^p以及交互式证明系统语言类MA,AM,IP等之间的30余种强分离关系作为本文结果的直接推论.     

SL(3,pn)的Cartan不变量

Let G = SL(3,K) be a simply connected, semi-simple algebraic group of type A₂ over an algebraically closed i'ield K of characteristic p>0. Let Γ_n = SL(3,pⁿ) be a finite subgroup consisting of fixed points of the Frobenius morphism F² of G.     

铋钙锶铜氧高温超导体的纳米结构特点

利用X衍射,X能量散射谱(EDS)和高分辨电子显微镜研究了3种Bi-Ca-Sr-Cu-O体系的超导材料及其纳米结构特点。除了具有a=5.41,b=5.44和c=30.8的正交晶胞作为基本结构A₁之外,还发现了3个与钙钛矿结构有关的结构类型:A₀,A₃和A₄。进而,并大量发现一个很显著的结构现象:A₁结构与那些钙钛矿有关的结构(A₀,A₂和A₄)发生共生长。     

Brouwer不动点定理与顶点在曲面上的四边形

设D是Euclid平面R² 中的一个半径为r的圆盘 ,F是D上Lipschitz连续的实值函数 ,A₁A₂ A₃ A₄是边长不超过r的等腰梯形 ,∠A₁A₂ A₃ =α≤π/ 2 .借助于Brouwer不动点定理证明了 :若F有一个Lipschitz常数λ≤min{1 ,tgα},则在曲面M ={(x ,y ,F(x ,y) )∈R³ ∶(x ,y)∈D}上存在共平面的四个点 ,它们张成一个与A₁A₂ A₃ A₄全等的四边形 .此外 ,还作了一些进一步的讨论 .     

关于R(Ax)闭的连续算子族Ax的Moore-Penrose广义逆Ax+连续的充要条件

设X是拓扑空间,A_x,闭值域R(A_x)为X→B(H)的连续映射,我们知道:即使在dim(H)有限的情况下,M.-P.逆A_x⁺:也不一定连续,A_x⁺连续的充要条件,对现代分析和应用数学的一些研究是很重要的,本文给出了,在一般拓扑空间X、局部紧拓扑空间X、A_x为Fredholm算子族等情况下,A_x⁺为连续的充分必要条件。     

关于广义Calderon－Zygmund算子

本文讨论了θ（ｔ）型和（ｌｏｇ，θ）型Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子在加权Ｈａｒｄｙ型空间ＨＡ_w^p上的有界性，θ（ｔ）型Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子在Ｈａｒｄｙ型加权块空间上的有界性，以及广义的ｗ－Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子是Ｈ^Ap_w到ＨＡ^p上的有界算子．     

二阶泛函微分方程的渐近性和振动性

本文讨论了二阶泛函微分方程的解的渐近性和振动性。文中指出,当sum from to +∞ (g^-1)(1/(r(t))dt<+∞时,(1)式的非振动解的渐近性态有且仅有如下的四种类型:A_c^k,A_c^∞,A_o^k,A_o^∞。当sum from to +∞ (g^-1)(1/(r(t))dt=+∞时,(1)式的非振动解的渐近性态有且仅有如下三种类型:A_c^o,A_∞^c,A_∞^c。在f为超线性或次线性的前提下,本文分别给出了存在A_c^k,A_c^∞,A_o^k,A_c^o,A_∞^c等型非振动解的充要条件。在f为强超线性或强次线性的前提下,本文给出了方程(1)为振动的充要条件。     

算子方程的解及算子张量积

本文讨论Hilbert空间上一类三阶二元算子方程组A^*AC = αA^*A² + βAA^*A;AA^*C = λA^*A² + γAA^*A,给出所有重交换的解(A,C).作为应用,得到算子张量积A(?)B+C(?)D和A₁(?)A₂(?)…(?)A_n为拟正规算子的充分必要条件.     

零禁带Hg1-xCdxTe受主杂质带导电

在不同磁场下,研究零禁带Hg_1-xCd_xTe的迁移率-温度曲线中的反常A₁,A₂.几方面的实验证明:A₁,A₂是由位于导带中的受主杂质浓度足够大形成杂质带所引起的,其中A₁起源于汞空位.     

二连通域上Besov函数的等价刻划

定义了二连通城上Besov函数，探讨了Besov函数的等价刻划，即给了函数为Besov函数的若干充要条件．     

Optimal factorization of Muckenhoupt weights

Peter Jones' theorem on the factorization of  weights is sharpened for weights with bounds near , allowing the factorization to be performed continuously near the limiting, unweighted case. When and is an  weight with bound , it is shown that there exist  weights  such that both the formula and the estimates hold. The square root in these estimates is also proven to be the correct asymptotic power as .

     

Correction to ``Optimal factorization of Muckenhoupt weights'

Peter Jones' theorem on the factorization of  weights is sharpened for weights with bounds near , allowing the factorization to be performed continuously near the limiting, unweighted case. When and is an  weight with bound , it is shown that there exist  weights  such that both the formula and the estimates hold. The square root in these estimates is also proven to be the correct asymptotic power as .

     

Poisson semigroup characterization and the trace theorem of a class of fractional mean oscillation spaces

In this paper, we use regular wavelets to study the Poisson extension of the fractional mean oscillation spaces . Via a distributional trace operator π_φ, we establish a relation between and a class of harmonic function spaces .     

Parabolic Equations with Measurable Coefficients

We investigate the unique solvability of second order parabolic equations in non-divergence form in , p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables. The second author was partially supported by NSF Grant DMS-0140405.     

Estimates of Oscillations of the Hardy Transform

For the Hardy transform of a nonincreasing function we obtain a sharp two-sided estimate of the BLO-norm and sharp inequalities between the BMO- and the BLO-norms of a nonincreasing function. A well-known lower bound for the BMO-norm of the Hardy transform is improved on the basis of these inequalities.     

Riesz rising sun lemma for several variables and the John-Nirenberg inequality

We obtain a multidimensional analog of the well-known Riesz rising sun lemma. We prove a more precise version of this lemma for space dimension d = 2 . We use these lemmas to establish an anisotropic analog of the John-Nirenberg inequality for functions of bounded mean oscillation with an exact constant in the exponent. Earlier, this exact constant was only known in the one-dimensional case.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 53–66.Original Russian Text Copyright © 2005 by A. A. Korenovskii.This revised version was published online in April 2005 with a corrected issue number.     

Compactness of composition operators on BMOA

A function theoretic characterization is given of when a composition operator is compact on BMOA, the space of analytic functions on the unit disk having radial limits that are of bounded mean oscillation on the unit circle. When the symbol of the composition operator is univalent, compactness on BMOA is shown to be equivalent to compactness on the Bloch space, and a characterization in terms of the geometry of the image of the disk under the symbol of the operator results.