共查询到10条相似文献,搜索用时 15 毫秒
1.
It is well known that the commutator Tb of the Calder′on-Zygmund singular integral operator is bounded on Lp(Rn) for 1 p +∞if and only if b∈BMO [1]. On the other hand, the commutator Tb is bounded from H1(Rn) into L1(Rn) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσbe the operators that its symbol is S01,δwith 0≤δ 1, if b∈LMO∞, then, the commutator [b, Tσ] is bounded from H1(Rn) into L1(Rn) and from L∞(Rn) into BMO(Rn); If [b, Tσ] is bounded from H1(Rn) into L1(Rn) or L∞(Rn) into BMO(Rn), then, b∈LMO_(loc). 相似文献
2.
Let L be a linear operator in L2(Rn) and generate an analytic semigroup {e-tL}t 0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0, ∞) be of upper type 1 and of critical lower type p0(ω) ∈ (n/(n + θ(L)), 1] and ρ(t) = t-1/ω-1(t-1) for t ∈ (0, ∞). We introduce the Orlicz-Hardy space Hω, L(Rn) and the BMO-type space BMOρ, L(Rn) and establish the John-Nirenberg inequality for BMOρ, L(Rn) functions and the duality relation between Hω, L(Rn) and BMOρ, L... 相似文献
3.
设A是Rn上的各向异性伸缩, L是由各向异性Calderón-Zygmund算子生成的一般的多线性算子.本文得到L从加权Lebesgue空间Lwp(Rn)到无权的各向异性Hardy空间HAp (Rn)的有界性.另外,对各向异性Hardy空间H1(Rn)和加权各向异性BMO空间BMOAw(Rn)得到包含关系:BMOAw(Rn)■(H1A(Rn))*.作为应用,对加权各向异性BMO函数b和各向异性Calderón-Zygmund算子T生成的交换子[T, b],得到‖[T, b](f)‖Lwp(Rn)C‖b‖BMOwA(Rn)‖f‖Lpw(Rn).以上所有结果在经典的各向齐性情形下也是新的. 相似文献
4.
建立了Marcinkiewicz积分从Hardy空间H1(Rn×Rm)到Lebesgue空间L1(Rn×Rm)的有界性,以及它们与Lipschitz函数所生成的交换子从Hardy空间H1(Rn×Rm)到Lebesgue空间Lq(Rn×Rm)的有界性,其中q>1. 相似文献
5.
胡国恩 《数学物理学报(B辑英文版)》2005,25(3):545-554
Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the Lp(Rn) boundedness (1<p<∞) and the weak type (H1(Rn), L1(Rn))boundedness for the corresponding commutators. A new interpolation theorem is also established. 相似文献
6.
Let L=-div(A▽) be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato square root L1/2 and b with ▽b∈Ln(Rn)(n> 2),is bounded from the homogenous Sobolev space L1p(Rn) to Lp(Rn)(p-(L) 相似文献
7.
YANG Dachun & ZHOU Yuan School of Mathematical Sciences Beijing Normal University Beijing China 《中国科学A辑(英文版)》2006,(6)
The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn×Rm) to the Lebesgue space L1(Rn×Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn×Rm) to the Lebesgue space Lq(Rn×Rm) for some q>1 相似文献
8.
设L是L2(Rn)上解析半群的无穷小生成算子,其积分核具有高斯界,L-α/2表示L的分数次积分算子,其中0<α<n.对自然数m,若bi(i=1,2,…,m)表示Rn上有界平均振荡函数,则由分数次积分L-α/2与bi(i=1,2,…,m)生成多线性交换子是从Lp(Rn)到Lq(Rn)是有界的,其中1<p<α/n,1/q=1/p-α/n. 相似文献
9.
The authors discuss problems of approximation to functions in L2(Rn) and operators fromL2(Rn1) to L2(Rn2) by Radial-Basis Functions. The results obtained solve the problem ofcapability of RBF neural networks, a basic problem in neural networks. 相似文献