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^*.     

Littlewood—Paley算子及Marcinkiewicz积分在Campanato空间εa,p上的有界性

我们证明了下述结果:若f∈ε^a,p,则适当限制参数值时,有g(f)(x)(S(f)(x),g_λ^*(f)(x),μ(f)(x))<∞a.e.,或者g(f)(x)(S(f)(x),g_λ^*(f)(x),μ(f)(x))<∞a.e.;并且在前者成立时,有g(f)(S(f),g_λ^*(f),μ(f))∈ε^a,p,以及‖g(f)‖_a,p     

关于g-函数的一些性质

本文得到的主要结果是:当f(x)∈BMO(Rⁿ)时,f的g-函数或者几乎处处发散,或者几乎处处取有限值;如属后者,则g(f)∈BMO(Rⁿ),且||g(f)||_*c||f||_*,而c只与空间维数有关。     

关于非线性泛函的一个问题

Suppose that H is a Hilbert space, D is a convex closed set inis a functioal, f(x)=1/2‖x‖²-g(x). Suppose that the minimum of f(x) withrespect to D is attained at x₀∈D and f(x) has a bounded linear Gateaux differential at x₀. In this paper we prove that f(x₀) is a critical value of f(x) when and only when g′(x₀)∈I_D(x₀)={(1-λ)x₀+λy|y∈D.λ≥0}.     

多元Szász—Mirkjan算子的一致逼近

本文研究了多元Szása—Mirakjan算子在C_2B(T)中的逼近性质,利用K—泛函,建立了等价的逼近定理.主要结果如下 定理设f∈C_2B(T),0a) ;(ii)‖S_n,m(f)-f‖_∞ =0(n^-a);(iii)a)‖f(x+tφ(x),y)-2f(x,y)+f(x-tφ(x),y)‖_∞ =0(t<     

紧Lie群上Hp（0＜P＜1）函数的临界阶Bochner－Riesz平均算子的有界性

本文利用尺度‖·‖_H(p,∞)研究了一般紧Ｌｉｅ群上Ｈ^p函数的临界阶Ｂｏｃｈｎｅｒ－Ｒｉｅｓｚ平均算子σ_R^δ:f→σ_R^δf的有界性，得到了如下结果：σ_R^δ是（Ｈ^p，Ｈ（ｐ，∞））型的，并且‖σ_R^δf‖_H(p,∞)≤C‖f‖_H^p     

极大高阶交换子的端点估计

该文主要确立了当b∈BMO 时, 极大高阶奇异积分算子交换子T_{b, m}* 满足如下不等式 |{y∈Rⁿ:T_{b, m}*f(y)>λ}|≤C||b||^m_BMO∫_Rⁿ|f(y)|/λ (1+log⁺|f(y)|/λ)^mdy 且T_{b, m}* 在L^p(Rⁿ)(1 < p <∞上有界.     

三角域上Bernstein多项式的Lipschitz常数

设T是平面上以T₁,T₂,T₃为顶点的三角形,f(p)为定义在T上的函数,称Bⁿ(f,P):=(?)f(i/n,j/n,k/n)B_i,j,kⁿ(P),为f的n次Bernstein多项式,这儿B_i,j,kⁿ(P):(n!)/(i!j!k!)uⁱv^jω^k是Bernstein基函数,(u,v,w)是P关于T的重心坐标。 B.M.Brown等人对单变量的Bernstein多项式证明了如果f∈Lip_Aλ,0<λ≤1,则对所有的n,都有B^α(f,x)∈Lip_Aλ。本文的目的是对定义在三角域T:{(x,y):x≥0,y≥0,x+y≤1}上的Bernstein多项式证明了类似的结果: 设f(P)∈Lip_Aλ,0<λ≤1,则对所有的n,Bⁿ(f,P)∈Lip_(2^1/2λA)λ,并且,在一定意义上,常数2^1/2λA是最好的。 上述结果对于任意的锐角或直角三角形T,也是成立的。 最后还指出,当T可为钝角三角形时,则不存在同一常数C,使对所有的n和任意三角形T,有Bⁿ(f,P)∈Lip_cλ。     

正规算子和亚正规算子的一些特征

In this paper it is proved that if T is a bounded linear operator on a Hilbert space H and λ(?)c1(W(T)), where cl(W(T)) is the closure of W(T)={(Tx, x); x∈H, ‖x‖ =1}, then T is normal iff U_λ=(T-λ)^*-1 (T-λ) is hyponormal and T is hyponormal iff U_λ=(T-λ)^*-1 (T-λ) is normaliod.     

齐次超曲面上测度Fourier变换的平均衰减估计

该文主要考虑限制在齐次超曲面上的测度dμ的Fourier变换的L^q范数估计. 基于此结论, 还得到了一些有关卷积算子Tf(x, θ)=f *μ_θ(x)的混合范数不等式.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Birational aspects of the geometry of Varieties of Sums of Powers

Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.