$\tilde{\rho}$混合样本下非参数核回归估计的渐近性质

本文在$\tilde{\rho}$混合样本下讨论Priestley和CHAO(1972)提出的一类非参数核回归估计的渐近性质, 在较弱的条件下证明了该估计的完全收敛性与强相合性.     

正则函数的修正的Cauchy型积分算子的不动点定理及迭代构造

本文第一部分讨论了正则函数的{\small Cauchy}型积分算子$T[f]$的{\small H\"{o}lder}连续性及此积分算子$T[f]$的范数与$f$的范数之间的关系.第二部分引入了修正的Cauchy型积分算子$\small \widetilde{T}$,首先利用压缩映射原理证明了$\small \widetilde{T}$算子具有不动点,然后给出了其不动点的迭代序列并证明了此序列强收敛于$\small \widetilde{T}$算子的不动点.     

关于算子的Orlicz-Hardy空间

设$L$为$L^2({{\mathbb R}^n})$上的线性算子且$L$生成的解析半群 $\{e^{-tL}\}_{t\ge 0}$的核满足Poisson型上界估计, 其衰减性由$\theta(L)\in(0,\infty)$刻画. 又设$\omega$为定义在$(0,\infty)$上的$1$-\!上型及临界 $\widetilde p_0(\omega)$-\!下型函数, 其中 $\widetilde p_0(\omega)\in (n/(n+\theta(L)), 1]$. 并记 $\rho(t)={t^{-1}}/\omega^{-1}(t^{-1})$, 其中$t\in (0,\infty).$ 本文引入了一类 Orlicz-Hardy空间 $H_{\omega,\,L}({\mathbb R}^n)$及 $\mathrm{BMO}$-\!型空间${\mathrm{BMO}_{\rho,\,L} ({\mathbb R}^n)}$, 并建立了关于${\mathrm{BMO}_{\rho,\,L}({\mathbb R}^n)}$函数的John-Nirenberg不等式及 $H_{\omega,\,L}({\mathbb R}^n)$与 $\mathrm{BMO}_{\rho,\,L^\ast}({\mathbb R}^n)$的对偶关系, 其中 $L^\ast$为$L$在$L^2({\mathbb R}^n)$中的共轭算子. 利用该对偶关系, 本文进一步获得了$\mathrm{BMO}_{\rho,\,L^\ast}(\rn)$的$\ro$-\!Carleson 测度特征及 $H_{\omega,\,L}({\mathbb R}^n)$的分子特征, 并通过后者建立了广义分数次积分算子 $L^{-\gamma}_\rho$从$H_{\omega,\,L}({\mathbb R}^n)$到 $H_L^1({\mathbb R}^n)$或$L^q({\mathbb R}^n)$的有界性, 其中$q>1$, $H_L^1({\mathbb R}^n)$为Auscher, Duong 和 McIntosh引入的Hardy空间. 如取$\omega(t)=t^p$,其中$t\in(0,\infty)$及$p\in(n/(n+\theta(L)), 1]$, 则所得结果推广了已有的结果.     

从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)$的加权复合算子

设$u \in H(D), \ \phi$为$D$上的解析自映射,定义$H(D)$上的加权复合算子为$u C_{\phi}(f)=$$uf\circ\phi$, \ $f\in H(D)$.本文得到了从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)\ (A_{0}^{\infty}(\varphi))$的加权复合算子$u C_{\phi}$的有界性和紧性的充要条件.     

非齐性广义Morrey空间上双线性强奇异Calder\''{o}n-Zygmund算子及交换子

本文的主要建立非齐性度量测度空间上双线性强奇异积分算子$\widetilde{T}$及交换子$\widetilde{T}_{b_{1},b_{2}}$在广义Morrey空间$M^{u}_{p}(\mu)$上的有界性. 在假设Lebesgue可测函数$u, u_{1}, u_{2}\in\mathbb{W}_{\tau}$, $u_{1}u_{2}=u$,且$\tau\in(0,2)$. 证明了算子$\widetilde{T}$是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到空间$M^{u}_{p}(\mu)$有界的, 也是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到广义弱Morrey空间$WM^{u}_{p}(\mu)$有界的,其中$\frac{1}{p}=\frac{1}{p_{1}}+\frac{1}{p_{2}}$及$1相似文献   

$\mathbb{C}^n$中单位球上$\rho$次抛物星形映射的一些估计

主要研究了$\mathbb{C}^n$中单位球$B^{n}$上$\rho \ (\rho \in [0,1))$次抛物星形映射的一些几何性质, 给出了该映射类的增长定理和掩盖定理, 及其齐次展开式中二次项的一些估计.     

$\mathbb{C}^{n}$中$\mu$-Bergman空间的刻画和微分复合算子

设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画; 然后 分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的 微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为 $A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件.     

$\rho$-混合序列移动平均过程的完全矩收敛的收敛速率[英文]

本文在适当的矩条件下, 通过利用$\rho$-混合序列移动平均过程的中心极限定理及其矩不等式,采用多重截尾的方法, 获得了$\rho$-混合序列关于移动平均过程完全矩收敛的收敛速率相关结论, 扩大了应用范围.     

Bessel函数的一个积分估计及其应用

推广了 Calder\’{o}n-Zygmund 的结果, 给出一个新的Bessel函数积分估计. 应用这个结果证明了变量核的参数型Marcinkiewicz积分 $\mu_{\Omega}^{\rho}$ 的 $L^{2}$ 有界性,其中核函数$\Omega$ 在 $\mathbb{R}^{n}$的单位球面$S^{n-1}$上没有任何光滑性.     

Cn中单位球上$mu$-Bloch函数的等价刻画

设$\mu$是$[0,1)$上的正规函数, 给出了${\bf C}^{\it n}$中单位球$B$上$\mu$-Bloch空间$\beta_{\mu}$中函数的几种刻画. 证明了下列条件是等价的: (1) $f\in \beta_{\mu}$; \ (2) $f\in H(B)$且函数$\mu(|z|)(1-|z|^{2})^{\gamma-1}R^{\alpha,\gamma}f(z)$ 在$B$上有界; (3) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{1}-1}\frac{\partial^{M_{1}} f}{\partial z^{m}}(z)}$ 在$B$上有界, 其中$|m|=M_{1}$; (4) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{2}-1}R^{(M_{2})}f(z)}$ 在$B$上有界.     

New estimates of continuity in $$M/GI/1/ \infty$$ queues

The paper deals with an estimation of the total variation distance between stationary distributions of waiting time in two queueing systems with equal Poisson inputs and different distributions B and $\widetilde B$ of service time. Assuming equality of two first moments of B and $\widetilde B$ the continuity inequalities are derived in terms of difference pseudomoments of B and $\widetilde B$ . When in addition the third moments of B and $\widetilde B$ coincide then the constant involved in the corresponding inequality has the asymptotics ${\text{O}}\left[ {\left( {1 - \rho } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} } \right]$ in the heavy traffic limit $\rho \to 1$ .     

On the spectral norm of algebraic numbers

In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $.     

The Groupoidal Analogue \widetilde{{\Theta}} to Joyal’s Category Θ is a Test Category

We introduce the groupoidal analogue $\widetilde{\Theta}$ to Joyal’s cell category Θ and we prove that $\widetilde{\Theta}$ is a strict test category in the sense of Grothendieck. This implies that presheaves on $\widetilde{\Theta}$ model homotopy types in a canonical way. We also prove that the canonical functor from Θ to $\widetilde{\Theta}$ is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on $\widetilde{\Theta}$ to weak equivalences of presheaves on Θ. Our proofs apply to other categories analogous to Θ.     

BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES

The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, the Φ-function nequalitities of sharp operators f_p~#, f_p~#, p-variation operators W_p, W_p and the martingale tranform operator T_v are discussed. It is proved that the boundedness of these operators characterizes the smoothness, convexity and UMD-property of Banach spaces.     

Bounds in Total Variation Distance for Discrete-time Processes on the Sequence Space

Potential Analysis - Let $\mathbb {P}$ and $\widetilde {\mathbb {P}}$ be the laws of two discrete-time stochastic processes defined on the sequence space $S^{\mathbb N}$, where S is a finite set of...     

关于 ``Banach spaces failing the almost isometric universal extension property'' 的一个注记

D.M. Speegle 在文献[1] 中给出了具有常数 $\alpha$的性质${\cal A}$ 的定义,并且证明了任意无限维的可分一致光滑Banach空间都具有这样的性质,而且常数 $\alpha\in [0,1)$.本文给出了一个使得无限维可分Banach空间具有这种性质的充分条件,以及几个关于文献[1] 的注解.     

$*$-双单型$A \omega^2$-半群的同构定理

在本文中,我们研究了满足条件$D^*=D(~)$的*-双单型$A\omega^2$-半群的同构,给出了它们之间的同构定理.     

σ-相关同伦元素的非平凡性

本文中,通过几何方法证明了σ相关同伦元素在球面稳定同伦群π_mS中是非平凡的,其中m=p~(n+1)q+2p~nq+(s+3)p~2q+(s+3)pq+(s+3)q-8,p≥7是奇素数,n3,0≤sp-3,且q=2(p-1).该σ相关同伦元素在Adams谱序列的E_2-项中由■_s+3■_ng0表示.