1) Lipschitz-zygmund classes
Lipschitz-Zygmund类
2) Zygmund class
Zygmund类
1.
The main result of this article is:For any Zygmund class C~(p,Z) map f:R~n→R~m if (n-m)/2≤p≤n-m-1,then either mesK_f>0 or mesC_f>0.
该文的主要结果是:对任意Zygmund类C~(p,Z)映射f:R~n→R~m,若(n-m)/2≤p≤n-m-1,则有mesK_f>0或者mesC_f>0。
3) Lipschitz class
Lipschitz类
1.
The properties of the positive linear periodic convolution operators Ln(f,x) such as convexity,monotone and Lipschitz class can be preserved in C2π space.
研究了正线性周期卷积算子Ln(f,x)在C2π空间中保持函数的单调性、凸(凹)性、Lipschitz类的性质,所得到的结果包含了文献《Fejer算子在C2π空间的若干性质》中的结果。
2.
This paper defines the bivariate Bernstein-Sikkema operators on the square and on the simplex,and studies an important property:the operators and the given functions are of the same Lipschitz class.
定义了正方形和单纯形上的二元Bernstein-Sikkema算子,研究了其一个重要的性质:函数与算子属于同一个Lipschitz类,其结果包含了文献《正方形上的Lipschitz连续函数的Bernstein多项式的常数Lipschitz》中的结果。
3.
By the monotonicity of continuity modulus,the properties of a kind of generalized Bernstein operators preserving some characters of the function related to monotonicity,convexity,Lipschitz class and modulus of continuity are discussed.
借助连续模的单调性,讨论一类广义Bernstein算子对函数的单调性、凸性、Lipschitz类及连续模等几个保持性质。
4) Caldern-Zygmund decomposition
Caldern-Zygmund分解
5) Calderon-Zygmund operator
Calderon-Zygmund算子
1.
We obtain the boundedness of higher order Calderon-Zygmund operators on a class test-function spaces.
本文得到了高阶 Calderon-Zygmund算子在一类检验函数空间上的有界
2.
Using the atomic decomposition and the molecule decomposition of Hardy space, the boundedness of Calderon-Zygmund operators of spaces of homegeneous type on Hardy spaces were proved.
利用 Hardy空间的原子分解与分子分解 ,证明了齐型空间上 Calderon-Zygmund算子在 Hardy空间上的有界性 。
6) Calderón-Zygmund operator
Calderón-Zygmund算子
1.
A new Hardy space H_b~p,where b is a pars- accretive function,was recently introduced and the boundedness of Calderón-Zygmund operators T from the classical Hardy space H~p to the new Hardy space H_b~p was also proven if T~* (b) = 0.
众所周知,如果Calderón-Zygmund算子T满足T~*(1)=0,则算子T在H~p,n/(n+ε)
2.
As an appli- cation,the authors prove that the commutators generated by Calderón-Zygmund operators with Osc_(exp L~r) (μ) functions for r≥1 satisfy the same weak estimates,where Osc_(exp L~r) (μ) RBMO(μ)с if r>1 and Osc_(exp L~r)(μ)=RBMO(μ) if r=1.
作为应用,证明了由Calderón-Zygmund算子和Osc_(exp L~r)(μ)函数生成的交换子在弱Herz空间中的弱型估计,其中r≥1。
3.
The theory of singular integrals especially the commutator of Calderón-Zygmund operator has been extensively applied to the partial differential equations and other pertinent fields.
奇异积分理论特别是Calderón-Zygmund算子广泛应用于偏微分方程及其它相关领域的研究。
补充资料：Lipschitz积分条件
Lipschitz积分条件
Lipsdnte integral condition
U尹如忱积分条件〔U脚而匕加魄阿“旧击柱门;刀‘四.职yc加哪似犯印目1.刃oel 以积分度量给出的关于函数增长性态的一种限制.称空间L，(a，b)(p笋l)中的函数f在[a，b1上满足具有常数M>O的二>0阶UpschjtZ积分条件，如果对所有h钊0，b一a)，有 {了“，，(一卜，(·)}，己·}”’一;(·)记作f〔LiP、(:，夕)，f〔H二(M)或f任LiP(“，尸)，f〔H二·对于周期函数(以b一a为周期)情形，可类似地定义Li讲ehitZ积分条件，只是不等式(*)中的积分上限b一h必须代之以b.
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参考词条