A LIPSCHITZ ESTIMATE FOR MULTILINEAR OSCILLATORY SINGULAR INTEGRALS WITH ROUGH KERNELS

In this paper, for the multilinear oscillatory singular integral operators TA1,A2,..,Ar defined by (x) where P(x,y) is a nontrivial and real-valued polynomial defined on Rn × Rn, Ω(x) is homogeneous of degree zero on Rn, As(x) has derivatives of order ms in ∧βs (0 ＜βs ＜1),Rms 1 (As; x, y) denotes the (ms 1)-st remainder of the Taylor series of As at x expended about y(s=1,2,…,r),M=∑rs=1ms, the author proves that if 0<β=∑rs=1βs<1, and Ω∈ Lq(Sn-1) for some q ＞ 1/(1 - β), then for any p ∈ (1, ∞), and some appropriate 0 ＜ β ＜ 1, TA1,A2,…,Ar is bounded on Lp(Rn).     

BMO ESTIMATES FOR MULTILINEAR FRACTIONAL INTEGRALS

In this paper,the authors prove that the multilinear fractional integral operator T A 1,A 2 ,α and the relevant maximal operator M A 1,A 2 ,α with rough kernel are both bounded from L p (1 p ∞) to L q and from L p to L n/(n α),∞ with power weight,respectively,where T A 1,A 2 ,α (f)(x)=R n R m 1 (A 1 ;x,y)R m 2 (A 2 ;x,y) | x y | n α +m 1 +m 2 2 (x y) f (y)dy and M A 1,A 2 ,α (f)(x)=sup r0 1 r n α +m 1 +m 2 2 | x y | r 2 ∏ i=1 R m i (A i ;x,y)(x y) f (y) | dy,and 0 α n, ∈ L s (S n 1) (s ≥ 1) is a homogeneous function of degree zero in R n,A i is a function defined on R n and R m i (A i ;x,y) denotes the m i t h remainder of Taylor series of A i at x about y.More precisely,R m i (A i ;x,y)=A i (x) ∑ | γ | m i 1 γ ! D γ A i (y)(x y) r,where D γ (A i) ∈ BMO(R n) for | γ |=m i 1(m i 1),i=1,2.     

具广义Calderón-Zygmund核的多线性振荡奇异积分极大算子的有界性

本文研究了具有广义Calderon-Zygmund核的多线性奇异积分极大算子和多线性振荡奇异积分极 大算子,证明了这类极大算子的Lp-有界性．     

多重奇异积分与Lipschitz函数生成的多线性交换子

本文研究了由多重奇异积分和Lipschitz函数生成的多线性交换子.利用Hardy-Littlewood极大算子的有界性,得到了交换子从Lebesgue积空间到Lebesgue空间的有界性,推广了文献[16]的结果.     

LIPSCHITZ ESTIMATES FOR MULTILINEAR SINGULAR INTEGRALS,II

In this paper, the authors study two classes of multilinear singular integrals and obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herz type spaces to central Campanato spaces. Moreover, the authors also consider the extreme cases.     

WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDERON-ZYGMUND OPERATORS

In this paper, some weighted estimates with general weights are established for the m-linear Caldern-Zygmund operator and the corresponding maximal operator. It is proved that, if p1 , ··· , pm ∈ [1, ∞] and p ∈ (0, ∞) with 1/p = ∑m k=1 1/pk , then for any weight w, integer ■with 1 ≤■≤ m, these operators are bounded from L p 1 (Rn , MBw) ×···× Lp■(Rn , MBw) × Lp +1 (Rn , Mw) ×···× Lp m (Rn , Mw) to Lp, ∞ (R n , w) or L p (R n , w), where B is a Young function and M B is the maximal operator associated with B.     

带振荡核奇异积分算子交换子在加权Morrey空间中的有界性质

本文研究Morrey空间中的交换子有界性的问题.利用John-Nirenberg不等式等工具建立带振荡核的奇异积分算子与BMO函数生成交换子在加权Morrey空间中的加权估计.     

COMMUTATORS OF SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS

Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 ＜ p ＜∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b, T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 ＜ p ＜∞.The condition of this paper is weaker than the usual pointwise Hormander condition.     

WEIGHTED ESTIMATES FOR COMMUTATORS OF MULTILINEAR CALDERON-ZYGMUND OPERATORS WITH NON-DOUBLING MEASURES

Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO（μ） functions.     

NON-STANDARD COMMUTATORS FOR ROUGH OSCILLATORY SINGULAR INTEGRALS

In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 〈 p 〈 ∞, the L^p-boundedness of such operators are obtained provided that their kernels belong to the spaces L^q（s^n-1） for some q 〉 1.     

Multi-weight, Weighted Weak Type Estimates for the Multilinear Calderón-Zygmund Operators

Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) × ··· × Lpm(Rn, vm) to Lp,∞(Rn, u).     

Sharp maximal function estimates for multilinear singular integrals with non-smooth kernels

In this article we obtain weighted norm estimates for multilinear singular integrals with non-smooth kernels and the boundedness of certain multilinear commutators by making use of a sharp maximal function.     

分数次积分交换子的加权Hardy型估计

本文研究了分数次积分交换子的加权Hardy型估计.利用加权Hardy空间的原子分解理论,得到了分数次积分算子与加权Lipschitz函数生成的交换子在加权Hardy空间上的有界性质,推广了陆善镇等在2002年中国科学A上的结果.     

A Weighted Weak Type Endpoint Estimate for the Multilinear Calderón-Zygmund Operators and Its Applications

A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel,which was introduced by Coifman and Meyer.As applications,the mapping properties on weighted L~(P1)(R~n)×…×L~(Pm)(R~n)with weight MBω for certain maximal operator MB and general weight ω,and a two-weight weighted norm estimate for this operator,are obtained.     

SOME ENDPOINT ESTIMATES FOR COMMUTATORS OFθ-TYPE CALDERON-ZYGMUND OPERATORS

In this note, the authors prove that the commutator T→b generated by 0-type Calder6n-Zygmund operator T and a Lipschitz function b→ is bounded from LP(Rn) into Lip(β-n/p)(Rn) and also maps from Ln/β(Rn) into BMO(Rn).     

各向异性函数空间上的多线性算子的估计及其应用

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Lp(Rn)到无权的各向异性Hardy空间HpA(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BMOwA(Rn)得到包含关系:BMOX(Rn)(...     

The Weighted Morrey Boundedness of Multilinear Singular Integral Operators on RD-Spaces

An RD-space $\mathcal{X}$ is a space of homogeneous type in the sense of Coifman and Weiss, which is equipped with a measure satisfying an additional reverse doubling property. In this paper we study the boundedness of multilinear singular integral operators in weighted Morrey spaces within the framework of RD-spaces.     

INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

It is proved that, for the nondivergence elliptic equations ∑in, j=1 aijuxixj = f,if f belongs to the generalized Morrey spaces Lp,ψ(ω), then uxixj ∈ Lp,ψ(ω), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp,ψ (ω).     

含Hilbert核的奇异积分带重结点的求积公式

本文讨论了Ｈｅｒｍｉｔｅ三角插值问题利用Ｈｅｒｍｉｔｅ三角插值建立２π周期函数正常积分带重结点的求积公式，用分离奇异点的方法建立了含Ｈｉｌｌｂｅｒｔ核的奇积分带重结点的求积公式。