Anisotropic norms of dirichlet kernels and some other trigonometric polynomials

In the paper new estimates of anisotropic norms for trigonometric polynomials are obtained. Translated fromMatematischeskie Zametki, Vol. 67, No. 5, pp. 686–701, May, 2000.     

EDGEWORTH EXPANSION FOR NEAREST NEIGHBOR- KERNEL ESTIMATE AND RANDOM WEIGHTING APPROXIMATION OF CONDITIONAL DENSITY

§ 1　 IntroductionThere are many discussions on the estimate of density,for example,the kernel andnearest neighbor estimates.Reference [1 ] gave the nearest neighbor-kernel estimate ofconditional density.[2 ] discussed the properties on the nearest neighbor-kernel estimateand bootstrap approximation of conditional density.[3 ] studied some asymptotical proper-ties on kernel estimate and random weighting approximation of density.In this paper,wewill discuss the properties of the nearest neighb…     

带粗糙核的Marcinkiewicz积分算子在加权Herz空间中的有界性

讨论了一类带有粗糙核的Marcinkiewicz积分算子在加权Herz空间上的有界性.     

变量核奇异积分和分数次微分加权范不等式

用T和D^γ（0 ≤ γ ≤ 1）分别表示变量核奇异积分和分数次微分算子.T^*和T^#分别为T的共轭算子及拟共轭算子.利用球调和多项式展式，本文得到了TD^γ-D^γT和（T^*-T^#）D^γ在?^q，λ_ω（Rⁿ）上的有界性.同时也得到了变量核奇异积分的积T₁T₂和拟积T₁°T₂的加权范不等式.     

L^p Estimates for Singular Radon Transforms with Rough Kernels

The purpose of this paper is to study the mapping properties of the singular Radon transforms with rough kernels. Such singular integral operators are proved to be bounded on Lebesgue spaces.     

Cn中有界域的Bergman核函数的零点问题

多复变数空间Cn中有界域的Bergman核函数的零点问题集中表现为陆启铿猜想.陆启铿猜想是波兰数学家M.Skwarczynski对陆启铿1966年的一篇文章中关于Bergman核函数的零点问题而命名的,至今已经40年了.该猜想已写入了多复变函数论的多本专著,引起很多数学家的兴趣而研究之,已经成为多复变函数论中的一个活跃的研究方向.本文简述了陆启铿猜想的最初含意,综述了迄今为止关于有界域的Bergman核函数有无零点的各种研究成果以及所用的思想和方法.特别对近来出现的陆启铿猜想的新研究领域进行了较详细的阐述并在最后提出了关于陆启铿猜想的6个Open Problems,希望国内的年轻数学家对陆启铿猜想感到兴趣而研究之.     

Fractional Lévy processes on Gel’fand triple and stochastic integration

In this paper, we investigate the long-range dependence of fractional Lévy processes on Gel’fand triple and construct stochastic integral with respect to fractional Lévy processes for a class of deterministic integrands.      

NA样本的递归密度估计

设$\{X_n,n\geq 1\}$是一个严平稳的负相协的随机变量序列, 其概率密度函数为$f(x)$.本文讨论了$f(x)$的递归核估计量的联合渐近正态性.