Lipschitz空间上的加权复合算子

设D是复空间C中的单位圆盘,ψ是D到自身的一个全纯映射,ψ(z)是D上的全纯函数,0＜α＜1.本文给出了单位圆盘中Lipschitz空间Lipa(D)上由ψ和ψ诱导的加权复合算子Wψ,ψ的有界性及紧性的充要条件.     

多圆柱上的Bloch空间上的加权复合算子

利用泛函分析多复变方法．研究了多圆柱上Bloch空间的加权复合算子的一些性质．并且通过圆柱的全纯自映射φ及全纯函数ψ的一些特性．分别给出了多圆柱上Bloch空间上由φ及ψ确定的加权复合算子的有界性与紧性的充要条件．     

多圆柱上Bergman空间到Bloch空间的复合算子

设qo是单位多圆柱Dn到自身的—个全纯映射,ψ是Dn上的—个全纯函数．本文研究单位多圆柱上从Bergman空间Ap（Dn）到Bloch空间β（Dn）的加权复合算子Tψ,ψ通过全纯映射ψ和全纯函数ψ的函数特征。分别给出了单位多圆柱上从Bergman空间AP（Dn）到Bloch空间β（Dn）的加权复合算子Tψ,ψ有界性和紧性的充分必要条件．     

关于复平面上H∞空间,βp空间以及βp0空间的几个问题

本文讨论了单位圆中Hardy空间H∞到p-Bloch空间βp的复合算子T1,φ和加权复合算子Tψ,ψ的有界性,也讨论了H∞到小p-Bloch空间ββ的复合算子T1,ψ的有界性问题;另外还讨论了小p-Bloch空间到H∞空间的点乘子及小p-Bloch空间上复合算子的紧性等.     

Cn中单位球上μ-Bloch空间之间的加权复合算子

设μ和ν是[0,1)上两个正规函数,该文给出了Cn(n>1)中单位球上Bloch型空间βμ到βν之加权复合算子Tψ,(ψ)为有界算子和紧算子的充要条件.     

Hardy空间Hp(BN)上的加权复合算子

φ：BN→BN的全纯映射，ψ∈H（BN），其中H（BN）表示BN上全纯函数集合，定义加权复合算子Wφ，ψf=ψ（f φ），f∈H（BN）．本文研究了Hardy空间H^p（BN）上的加权复合算子的有界性、紧性、弱紧性以及完全连续性，给出了有界性、紧性的充要条件以及证明了紧性与弱紧性的等价关系．最后讨论了加权复合算子的完全连续性．     

BMOA到Bloch型空间的加权复合算子

给出了Cn中单位球上BMOA空间到Bloch型空间之加权复合算子Tψ,ψ为有界算子和紧算子的充要条件.     

p-Bloch空间上的复合算子和加权复合算子

本文系统地讨论了单位圆中p-Bloch空间上复合算子T1,ψ的有界性和紧性以及加权复合算子Tψ,ψ的有界性,同时也在小p-Bloch空间上讨论了复合算子T1,ψ的有界性问题.主要得到以下结论(i)Tψ,ψ是空间βp到βq的有界算子之充要条件;(ii)T1,ψ是空间βp到βq的紧算子之充要条件;(iii)T1,ψ是空间βp0到βq0的有界算子之充要条件等.从空间或算子上扩展了文[1,4]的相应结论.     

单位球Dirichlet空间上的交换对偶Toeplitz算子

研究对偶Toeplitz算子（半）交换时其符号的关系.通过对其符号的分解,借助多复变函数的有关理论,得到了单位球Dirichlet空间上以多重调和函数为符号的对偶Toeplitz算子Sψ与Sψ（半）交换的充要条件.     

关于复平面上H~∞空间,β~p空间以及β_0~p空间的几个问题

本文讨论了单位圆中Hardy空间H∞到p-Bloch空间βP的复合算子T1.φ加权复合算子Tψ,(?)的有界性,也讨论了H∞到小p-Bloch空间β6的复合算子T1,(?)的有界性问题;另外还讨论了小p-Bloch空间到H∞空间的点乘子及小p-Bloch空间上复合算子的紧性等.     

Estimation of the measure of the image of the ball

Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the rational approximation of the sum of the reciprocals of the Fermat numbers

Let $\mathcal{G}(z):=\sum_{n\geqslant0} z^{2^{n}}(1-z^{2^{n}})^{-1}$ denote the generating function of the ruler function, and $\mathcal {F}(z):=\sum_{n\geqslant} z^{2^{n}}(1+z^{2^{n}})^{-1}$ ; note that the special value $\mathcal{F}(1/2)$ is the sum of the reciprocals of the Fermat numbers $F_{n}:=2^{2^{n}}+1$ . The functions $\mathcal{F}(z)$ and $\mathcal{G}(z)$ as well as their special values have been studied by Mahler, Golomb, Schwarz, and Duverney; it is known that the numbers $\mathcal {F}(\alpha)$ and $\mathcal{G}(\alpha)$ are transcendental for all algebraic numbers α which satisfy 0<α<1. For a sequence u, denote the Hankel matrix $H_{n}^{p}(\mathbf {u}):=(u({p+i+j-2}))_{1\leqslant i,j\leqslant n}$ . Let α be a real number. The irrationality exponent μ(α) is defined as the supremum of the set of real numbers μ such that the inequality |α?p/q|<q ^?μ has infinitely many solutions (p,q)∈?×?. In this paper, we first prove that the determinants of $H_{n}^{1}(\mathbf {g})$ and $H_{n}^{1}(\mathbf{f})$ are nonzero for every n?1. We then use this result to prove that for b?2 the irrationality exponents $\mu(\mathcal{F}(1/b))$ and $\mu(\mathcal{G}(1/b))$ are equal to 2; in particular, the irrationality exponent of the sum of the reciprocals of the Fermat numbers is 2.     

Refinement of the asymptotics of the power of the quantile test

One investigates the asymptotic properties of the quantile test, similar to the properties of the Pearson's chi-square test of fit.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 5–15, 1986.The author is grateful to D. M. Chibisov for useful remarks.