1) 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。
2) Calderón-Zygmund operators
Calderón-Zygmund算子
1.
For a class of maximal commutators which are the variants of the usual maximal Calderón-Zygmund commutators associated with Calderón-Zygmund operators and Lipschitz functions,their boundedness in Lebesgue spaces is established and some endpoint estimates are obtained.
建立了一类与Calderón-Zygmund算子和Lipschitz函数相关的极大交换子在非齐型空间上的Lebesgue空间中的有界性以及某些端点估计。
2.
The boundedness is established of the commutators generated by Calderón-Zygmund operators or fractional integrals with RBMO(μ) functions or Lipschitz functions in Morrey spaces on nonhomogeneous spaces.
证明了由Calderón-Zygmund算子或分数次积分算子与RBMO(μ)函数以及Lipschitz函数生成的交换子在非齐型空间上的Morrey空间中的有界性。
3) generalized Calderón-Zygmund operator
广义Calderón-Zygmund算子
1.
Boundedness of commutators of generalized Calderón-Zygmund operators
广义Calderón-Zygmund算子交换子的有界性
2.
It is proved that the generalized Calderón-Zygmund operators of vector valued kernels are bounded and weighted bounded from Hardy spaces HK_p associated with Herz spaces to vector valued Herz spaces K_ E,p .
文中完善了参考文献[5]中的结论,在通常的标准假设下,证明了一类具有向量值核的广义Calderón-Zygmund算子从Herz型Hardy空间HKp到向量值Herz空间KE,p的有界性及加权有界性。
4) Multilinear Calderón-Zygmund operator
多线性Calderón-Zygmund算子
1.
Weighted L~p and endpoint estimates with general weights are established for the maximal operator associated with the multilinear Calderón-Zygmund operator introduced by Grafakos and Torres.
本文建立由Grafakos和Torrea引进的多线性Calderón-Zygmund算子相关极大算子的加权L~P(R~N)估计和弱端点估计。
6) θ(t) type Calderón-Zygmund operator
θ(t)型Calderón-Zygmund算子
1.
By the atomic decompositions,we get that the θ(t) type Calderón-Zygmund operators are bounded from H1,∞atb(μ) to L1(μ) and from L∞(μ) to RBMO(μ) for non-doubling measure.
本文研究了奇异积分算子在非双倍测度下的有界性问题,利用原子分解理论,证明了θ(t)型Calderón-Zygmund算子在非双倍测度下是从Hatb1,∞(μ)到L1(μ)以及从L∞(μ)到RBMO(μ)有界的。
2.
In this paper,under this assumption,the boundedness of the commutators of RBMO(μ) with θ(t) type Calderón-Zygmund operators from L∞(μ) to RBMO(μ) and from H1b(μ) to L1(μ) are established.
本文中,在这种非双倍测度下证明了RBMO(μ)与θ(t)型Calderón-Zygmund算子的交换子是L∞(μ)到RBMO(μ)有界的,同时还建立了该交换子H1b(μ)到L1(μ)的有界性。
补充资料：凹算子与凸算子
凹算子与凸算子
concave and convex operators
凹算子与凸算子「阴~皿d阴vex.耳阳.勿韶;.留叮.肠疽“‘.小啊j阅雌口叹甲司 半序空间中的非线性算子，类似于一个实变量的凹函数与凸函数. 一个Banach空间中的在某个锥K上是正的非线性算子A，称为凹的(concave)(更确切地，在K上u。凹的)，如果 l)对任何的非零元x任K，下面的不等式成立: a(x)u。(Ax续斑x)u。，这里u。是K的某个固定的非零元，以x)与口(x)是正的纯量函数; 2)对每个使得 at(x)u。续x《月1(x)u。，al，月l>0，成立的x‘K，下面的关系成立二 A(tx))(l+，(x，t))tA(x)，0
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参考词条