加权Bergman空间上Toeplitz与Hankel算子紧性的一个新特征

本文研究加权Ｂｅｒｇｍａｎ空间Ａ^（ｐ,α）（Ｂ）（ｐ＞１）上Ｔｏｅｐｌｉｔｚ与Ｈａｎｋｅｌ算子的紧性．证明了符号属于Ｌ^∞（Ｂ）的Ｔｏｅｐｌｉｔｚ与Ｈａｎｋｅｌ算子的紧性与作用空间Ａ^ｐ,α（Ｂ）无关     

加权BMO函数空间上的Hardy－Littlewood极大算子

本文给出了Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ极大函数和加权ＢＭＯ的有界性证明：即若f∈ＢＭＯ_w,w∈A_∞,且(?)Mf(x)<∞, 则M(f)(x) ∈BMO_w, 且‖Mf‖_w^*≤c‖f‖_w^*.     

一类全不连通群上的BMO和奇异积分算子

本文主要讨论了定义在局部紧的全不连通群Ｇ上的一类卷积算子在加权Ｌ^∞（Ｇ）和ＢＭＯ（ａ）空间的性态．证明了如果卷积算子的核满足适当的条件,则算子是Ｌ^∞（Ｇ）到ＢＭＯ（ａ）有界的或是ＢＭＯ（ａ）到ＢＭＯ（ａ）有界的．     

带粗糙核的多线性振荡奇异积分

本文考虑多线性算子ＴＡｆ（ｘ）＝∫ＲｎｅｉＰ（ｘ，ｙ）Ω（ｘ－ｙ）｜ｘ－ｙ｜ｎ＋ｍＲｍ＋１（Ａ；ｘ，ｙ）ｆ（ｙ）ｄｙ，ｎ２，其中Ｐ（ｘ，ｙ）是Ｒｎ×Ｒｎ中的实值多项式，Ω是零次齐次函数且满足ｍ阶消失性条件，Ｒｍ＋１（Ａ；ｘ，ｙ）＝Ａ（ｘ）－｜α｜ｍＤαＡ（ｙ）（ｘ－ｙ）α，对任何｜α｜＝ｍ，ＤαＡ∈ＢＭＯ（Ｒｎ）．证明了Ω∈Ｌｑ（Ｓｎ－１）且ｑ＞１时，对任何１＜ｐ＜∞，‖ＴＡｆ‖ｐＣ（ｎ，ｍ，ｐ，ｄｅｇＰ）｜α｜＝ｍ‖ＤαＡ‖ＢＭＯ‖ｆ‖ｐ     

椭圆中一类三角形面积最大值探求

椭圆中一类三角形面积最大值探求陶兴模（重庆市铜梁中学６３２５６０）设Ｍ（ｐ，ｑ）是椭圆内的一个定点．弦ＡＢ过定点Ｍ，如何求△ＡＯＢ面积的最大值呢？按照常规方法，先求出弦ＡＢ的长和ＡＢ边上的高，然后求面积函数的最大值．这种解法一般情况下是不易奏效的．本...     

空间两直线所成角的一个性质

平面Ｍ内的一条直线和平面Ｍ的斜线及其在Ｍ内的射影间所成的角有下述关系 :图 1　命题 1图命题 1　如图 1所示 .平面Ｍ内的一条直线ＢＣ和Ｍ的斜线ＰＡ成角θ ,ＢＣ与斜线ＰＡ在平面Ｍ内的射影ＯＡ成角 ,则1)当 0 <θ<π2 时 ,θ> ;2 )当 π2 <θ <π时 ,θ < ;3)当θ=π2 时 ,θ = .证　 1)如图 1,∠ＰＡＣ =θ ,且 0 <θ <π2 ,∠ＣＡＯ= .过点Ｐ作ＰＣ⊥ＢＣ于Ｃ ,连ＯＣ .由三垂线逆定理知ＯＣ⊥ＢＣ .显然由ｃｏｓ∠ＰＡＣ =ｃｏｓ∠ＰＡＯ·ｃｏｓ∠ＣＡＯ ,有ｃｏｓ∠ＰＡＣ <ｃｏｓ∠ＣＡＯ .∵在 ( 0 ,π)内余弦函数为…     

齐型空间上的T(1)定理和交换子

本文在齐型空间上讨论弱核形式的　Ｔ（１）　定理，　并得到弱核形式的奇异积分算子与　ＢＭＯ　函数的交换子的Ｌｐ有界性及端点估计　（１＜ｐ＜∞　）．     

映射F_p:X→‖AXB-C‖_p~p的临界点的特征

对于Ｈｉｌｂｅｒｔ空间上有界线性算子Ａ、Ｂ、Ｃ,考虑了当Ａ有一个广义逆Ａ~－使得（ＡＡ~－）~＊＝ＡＡ~－,Ｂ有一个广义逆 Ｂ~－使得（Ｂ~－ Ｂ）～＊＝ Ｂ~－ Ｂ时,映射 Ｆ_ｐ： Ｘ→｜｜ＡＸＢ－ Ｃ｜｜_ｐ~ｐ临界点的特征的一般形式（１＜ ｐ＜∞）,推广了Ｐ．Ｊ．Ｍａｈａｒ的关于对ｐ＝ ２时的结果,并指出该定理可推广到多个算子的情形．     

A THEOREM ON EMBEDDING W~(s,p) INTO L(np/n-sp).p

ＡＴＨＥＯＲＥＭＯＮＥＭＢＥＤＤＩＮＧＷ~（ｓ，ｐ）ＩＮＴＯＬ(np/n-sp).pＪｉａｎｇＭｉｎｇ（姜明）（Ｄｅｐｔ．Ａｐｐｌ．Ｍａｔｈ．ＢｅｉｊｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｂｅｉｊｉｎｇ１０００８１，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｔ...     

ASYMPTOTIC BEHAVIOR OF OPERATORS OF PROBABILISTIC TYPE IN L_p SPACES

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＯＰＥＲＡＴＯＲＳＯＦＰＲＯＢＡＢＩＬＩＳＴＩＣＴＹＰＥＩＮＬ_ｐＳＰＡＣＥＳ￥ＣＨＥＮＷＥＮＺＨＯＮＧ；ＣＵＩＺＨＥＮＬＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，Ｘｉ?..     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].