Estimates of commutators for multilinear operators on Herz-type spaces

In this paper, the boundedness of mulitilinear commutator [b,T] on Herz-type space is considered, where T is a standard Calderón-Zygmund singular operator and b ∈ (BMO(Rn))m.     

广义分数次积分多线性交换子的端点估计

设函数b=（b1,b2,…,bm）和广义分数次积分L-a／2（0〈α〈n）,它们生成多线性算子定义如下 Lb -a/2 f = [bm …, [b2[b1, L-a/2]],…, ]f,其中m ∈ Z＋ , bi ∈ Lipβi （0 〈βi 〈 1）,其中（1≤i≤m）．将讨论Lb -1a/2。从Mp^q（Rn）到Lip（α＋β-n/ q） （ Rn ）和q^q （ Rn ）到BMO（Rn）的有界性．     

粗糙核奇异积分交换子在Triebel-Lizorkin空间的有界性

应用核的分解,讨论了粗糙核奇异积分算子 Tf（x）=p.v.∫R^nΩ（x-y）/｜x-y｜^nf（y）dy 和BMO（R^n）函数b生成的交换子[b,T]的有界性．证明了当Ω∈L（logL）^2（S^n-1）时,[b,T]是Triebel—Lizorhn空间Fp^α,q（R^n）上的有界算子．     

非倍测度条件下由Marcinkiewicz积分与RBMO函数生成的交换子在Herz空间中的有界性

本文研究了非倍测度条件下的一类由Marcinkiewica积分与RBMO函数生成交换子的有界性.通过Marcinkiewica积分及该交换子在Lebesgue空间中的有界性,得到了此交换子在Herz空间中的有界性.     

Littlewood-Paley g-函数交换子的Hardy型估计

证明了当q>1时,Littlewood-Paley g-函数与LMO(BMO的一个子空间)函数的交换子g_(Ψ,b)是局部Hardy空间h~1(R~n)到空间h~1(R~n)+L~q(R~n)的一个连续映射.     

De Rham and Infinitesimal Cohomology in Kapranov's Model for Non commutative Algebraic Geometry

The title refers to the nilcommutative or NC-schemes introduced by M. Kapranov in Noncommutative Geometry Based on Commutator Expansions, J. Reine Angew. Math 505 (1998) 73–118. The latter are noncommutative nilpotent thickenings of commutative schemes. We also consider the parallel theory of nil-Poisson or NP-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for NC- and NP-schemes. The variants include nilcommutative and nil-Poisson versions of the de Rham complex as well as of the cohomology of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham Cohomology of Schemes, Dix exposés sur la cohomologie des schémas, Masson, Paris (1968), pp. 306–358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express the cohomology groups of a noncommutative scheme Y as a sum of copies of the usual (de Rham, infinitesimal) cohomology groups of the underlying commutative scheme X (Theorems 6.1, 6.4, 6.7). As a byproduct we obtain new proofs for classical results of Grothendieck (Corollary 6.2) and of Feigin and Tsygan (Corollary 6.8) on the relation between de Rham and infinitesimal cohomology and between the latter and periodic cyclic homology.     

WEAK TYPE（H^1 ,L^1） ESTIMATE FOR COMMUTATOR OF MARCINKIEWICZ INTEGRAL

Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO（R^n）. It is proved that μΩ,bis bounded from the Hardy space H^1 （R^n） into the weak L^1（R^n） space.     

Weighted weak type estimates for commutators of the Marcinkiewicz integrals

In this paper the authors give the weighted weak L logL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities for the Marcinkiewicz integral and its commutators with different weight functions are also discussed.     

Commutators of integral operators with variable kernels on Hardy spaces

LetT _Ω,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, T_Ω,α] be the commutator generated by T_Ω,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, T_Ω,α] on the Hardy spaces, under some assumptions such as theL ^r -Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators . The smoothness conditions imposed on are weaker than the corresponding known results.     

Generalized cyclic cohomology associated with deformed commutators

The generalized cyclic cohomology is introduced which is associated with -deformed commutators . Some formulas related to the trace of the product of -deformed commutators are established. The Chern character of odd dimension associated with -deformed commutators is studied.