多线性分数次奇异积分在弱 Hardy 空间的Lipschitz 估计

讨论了一类具有粗糙核多线性分数次奇异积分算子在弱 Hardy 空间的性质,通过原子分解,得到了这类算子在弱Hardy空间的有界性.     

多线性算子在Herz型Hardy空间上的有界性

本文证明了Ｒｎ上奇异积分乘积之有限和的多线性算子是从ＨＫｑ１α１,ｐ１（Ｒｎ）×… ×ＨＫｑｋαｋ,ｐｋ（Ｒｎ）到ＨＫｑα,ｐ（Ｒｎ）有界的,如果它满足由目标空间所确定的直到一定阶的消失矩条件．这些多线性算子所满足的消失矩条件,当αｊ≥０时也是必要的．而且,这里所考虑的奇异积分包括Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ奇异积分及任意阶的分数次积分．     

粗糙核分数次积分算子的多线性算子在Hardy空间上的有界性

该文证明带有粗糙核的分数次积分算子的多线性算子[T_{Omega,alpha}^{A}(f)(x)={rm {rm p.v.}}int_{R^{n}}P_{m}(A;x,y)frac{Omega(x-y)}{|x-y|^{n-alpha+m-1}}f(y){rm d}y]的$(H^{1}(rr^{n}),L^{frac{n}{n-alpha},infty}(rr^{n}))$有界性.     

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．     

变指数空间上多线性分数次积分的Lipschitz光滑性

本文研究了多线性分数次积分算子在变指数空间的有界性.利用多线性分数次积分转化为相对应的分数次积分的方法,获得了它从变指数强和弱Lebesgue空间到变指数Lipschitz空间的有界性,推广了先前的研究结果.     

弱Hardy空间上多线性分数次积分算子的有界性

本文研究了弱Hardy空间上多线性分数次积分算子和相应的多线性分数次极大算子的有界性,利用多线性分数次积分转化为相对应的分数次积分的方法,得到算子TΩ,α,A和MΩ,α,A的弱型估计.     

多线性奇异积分算子的加权Lipschitz估计

该文讨论了一类多线性积分算子的加权Lipschitz有界性,通过将多线性积分算子用相应的分数次积分估计,得到一种简明的证明方法.      

多线性分数次积分及其极大算子在变指标Herz空间上的有界性

本文研究了多线性分数次积分算子T_?,μ^A及其极大算子M_?,μ^A在变指标空间上的有界性.利用变指标Lebesgue空间和Lipschitz空间的相关性质,获得了这两类算子分别在变指标Herz空间和变指标Herz-Morrey空间上的有界性.这一结果推广了这两类算子在变指标Lebesgue空间上有界性的结论.     

多线性分数次积分算子交换子的有界性

本文利用sharp极大函数的估计,证明了一类由多线性分数次积分算子和BMO(Rn)函数生成的交换子的Lp(Rn)有界性.     

关于分数次Marcinkiewicz积分在Hardy空间上的有界性

本文研究了核函数粗糙的分数次Marcinkiewicz积分μΩ,α在Hardy空间上的有界性.利用Hardy空间的原子分解定理,获得了算子μΩ,α的H1,Ln-nα型和(Hp,Lq)型的有界性结果.     

The fractional multilinear singular integral with variable kernels on hardy spaces

The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from Lp to Hq.     

非倍测度条件下Marcinkiewicz积分及其交换子在Morrey空间中的有界性

讨论了测度μ在满足非倍条件下,Marcinkiewicz积分算子及其与RBMO（μ）函数、Lipschitz函数生成的交换子的有界性,通过Marcinkiewica积分及该交换子在Lebesgue空间中的有界性,得到了该算子及交换子在非齐型空间上的Morrey空间中的有界性．     

On boundedness of discrete multilinear singular integral operators

Let m(ξ,η) be a measurable locally bounded function defined in R². Let 1?p₁,q₁,p₂,q₂<∞ such that pi=1 implies qi=∞. Let also 0<p₃,q₃<∞ and 1/p=1/p₁+1/p₂−1/p₃. We prove the following transference result: the operator

     

THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS ON WEIGHTED SPACES AND HERZ-TYPE SPACES

The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon-Zygmund kernel on Herz-type spaces is also considered.     

A Cotlar type inequality for the multilinear singular integral operators and its applications

A Cotlar type inequality is established for the multilinear singular integral operators. As applications, some two-weight norm inequalities are obtained for the maximal operator corresponding to the multilinear singular integral operators.     

A note on the multilinear singular integral operators

Lp(Rn) boundedness is considered for the multilinear singular integral operator defined by TAf(x) = ∫Rn Ω(x - y)/|x - y|n 1 (A(x) - A(y) - (△)A(y)(x - y))f(y)dy,where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈ Lipα(Sn-1) (0 ＜α≤ 1) and implies the Lp(Rn) (1 ＜ p ＜ oo) boundedness for the operator TA. Some endpoint estimates are also established.     

Maximal operator for multilinear Calderón-Zygmund singular integral operators on weighted Hardy spaces

In this paper, the maximal operator associated with multilinear Calderón-Zygmund singular integral operators will be studied by using an improved Coltlar's inequality. Moreover, weighted norm inequalities and some estimates on weighted Hardy spaces are obtained for this maximal operator.     

On the boundedness of rough oscillatory singular integrals on Triebel-Lizorkin spaces

We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory integrals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions.     

Boundedness of the anisotropic maximal and anisotropic singular integral operators in generalized Morrey spaces

In this paper we give the conditions on the pair (ω ₁, ω ₂) which ensures the boundedness of the anisotropic maximal operator and anisotropic singular integral operators from one generalized Morrey space M_p,w1 \mathcal{M}_{p,\omega _1 } to another M_p,w2 \mathcal{M}_{p,\omega _2 }, 1 < p < g8, and from the space M_1,w1 \mathcal{M}_{1,\omega _1 } to the weak space WM_1,w2 W\mathcal{M}_{1,\omega _2 }.