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加权Besov嵌入中的线性随机宽度

浙江师范大学学报（自然科学版） 2014年第2期37卷 171-176页

作者：王晶晶钱李新浙江师范大学数理与信息工程学院浙江金华321004

研究了如下嵌入空间中的线性随机n-宽度:Bs1p1,q1(Rd,α)→Bs2p2,q2(Rd),1≤p1,p2,q1,q2≤∞,min(α,δ)>dmax(1/p2-1/p1,0).其中:δ=s1-s2-d(1/p1-1/p2);Bs1p1,q1(Rd,α)表示加权的Besov空间;权函数为ωα(x)=(1+|x|2)α/2,α>0.并且... 详细信息

关键词：线性随机宽度嵌入 Besov 空间权函数

Convergence Rates of Density Estimation in Besov Spaces

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Applied Mathematics 2011年第10期2卷 1258-1262页

作者： Huiying Wang 不详

The optimality of a density estimation on Besov spaces Bsr,q(R) for the Lp risk was established by Donoho, Johnstone, Kerkyacharian and Picard (“Density estimation by wavelet thresholding,” The Annals of Statistics, Vol. 24, No. 2, 1996, pp. 508-539.). To show the lower bound of optimal rates of convergence Rn(Bsr,q, p), they use Korostelev and Assouad lemmas. However, the conditions of those two lemmas are difficult to be verified. This paper aims to give another proof for that bound by using Fano’s Lemma, which looks a little simpler. In addition, our method can be used in many other statistical models for lower bounds of estimations.

关键词： Optimal Rate of Convergence Density Estimation Besov Spaces Wavelets

Besov spaces and Herz spaces on local fields

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Science China Mathematics 1998年第10期41卷 1051-1060页

作者：朱月萍郑维行 Department of Mathematics Nanjing University Nanjing China

The relationship of Besov spaces and Herz spaces on local fi elds is given. As an application, one multiplier theorem is obtained. And the de compositional characterization of the weighted Besov spaces is established.

关键词： Besov spaces Herz spaces local fields multiplier atom_ decomposition.

Average widths and optimal recovery of multivariate Besov classes in L_p(R^d)

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Chinese Science Bulletin 1998年第8期43卷 638-641页

作者： Yanjie Jiang Yongping Liu Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

Some weak asymptotic results for average σ-K width and average σ_L width of the isotropic Besov classes S r pθB(R d), S r pθb(R d) and the anisotropic Besov classes S r pθB(R d), S r pθb(R d) in L p(R d) (1≤p<... 详细信息

关键词： average dimension average width optimal recovery Besov class.

Cn中单位球上Mbius不变Besov空间中函数的增长性（英文）

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Chinese Quarterly Journal of Mathematics 2000年第1期15卷 36-42页

作者：胡鹏彦徐正彬深圳大学师范学院数学教育系!深圳　广东　518060 信阳教师进修学校!河南信阳464000

本文主要讨论Ｃ中单位球上Ｍｂｉｕｓ不变Ｂｅｓｏｖ空间中函数的增长性并给出其Ｔａｙｌｏｒ系数的估计．

关键词： Mbius变换不变 Besov p-空间 Bloch空间 Bergman度量

Periodic Solutions of Third-order Differential Equations with Finite Delay in Vector-valued Functional Spaces

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Acta Mathematica Sinica,English Series 2019年第1期35卷 105-122页

作者： Shang Quan BU Gang CAI Department of Mathematical Sciences Tsinghua UniversityBeijing 100084P.R.China School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331P.R.China

In this paper, we study the well-posedness of the third-order differential equation with finite delay(P3): αu’"(t) + u"(t) = Au(t) + Bu’(t) + Fut +f(t)(t ∈ T := [0,2π]) with periodic boundary conditions u(0) = u(2π), u’(0) = u"(2π),u"(0)=u"(2π) in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces Bp,qs(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠ Besov, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp([-2π, 0];X)(resp. Bp,qs([-2π, 0];X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. Bp,qs-well-posedness)of(P3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.

关键词： Well-posedness delay equations Fourier multiplier Lebesgue-Bochner spaces Besov spaces

A Characterization of Besov Spaces of Para-Accretive Type and Its Application

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Applied Mathematics 2017年第4期8卷 590-606页

作者： Junxian Li Kunchuan Wang Department of Applied Mathematics National Dong Hwa University Taiwan

There are two folds in this article. One fold is to characterize the Besov spaces of para-accretive type , which reduces to the classical Besov spaces when the para-accretive function is constant, by using a discrete Calderón-type reproducing formula and Plancherel-P?lya-type inequality associated to a para-accretive function b in Rn. The other is to show that a generalized singular integral operator T with extends to be bounded from for and , where ε is the regularity exponent of the kernel of T.

关键词： Besov Space Calderón Reproducing Formula Para-Accretive Function Tb Theorem Triebel-Lizorkin Space

Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces

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Frontiers of Mathematics in China 2019年第1期14卷 95-122页

作者： Feng LIU Zunwei FU Seong Tae JHANG College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao 266590 China Department of Mathematics Linyi University Linyi 276005 China School of Mathematical Sciences Qufu Normal University Qufu 273100 China Department of Computer Science The Univers计y of Suwon Wau-ri Bongdam-eup Hwaseong-si Gyeonggi-do 445-743 Korea

We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case.

关键词： Parametric Marcinkiewicz integral homogeneous mapping Triebel- Lizorkin space Besov space

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各向异性密度函数的小波估计

山东大学学报（理学版） 2019年第6期54卷 99-105页

作者：曹凯凯北京工业大学应用数理学院

基于小波方法在各向异性 Besov 空间中研究了非紧支密度函数的估计问题,给出线性小波估计器,并证明其在 Lp ( 2≤ p <+∞)风险意义下的上界。进一步地,假定密度函数具有独立结构来降低维数灾难,并给出相应上界证明。

关键词：小波密度估计各向异性独立结构 Besov 空间