ON MULTILINEAR COMMUTATORS OF Θ-TYPE CALDERóN-ZYGMUND OPERATORS

In this paper, we discuss the multilinear commutator of Θ-type Calder6n- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from LP（Rn） to Lq（Rn）, from LP（Rn） to Triebel-Lizorkin spaces and on certain Hardy type spaces.

THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS FROM L^p(R^n) TO TRIEBEL-LIZORKIN SPACES

Let b^→=（b1,…,bm）,bi∈∧°βi（R^n）,1≤i≤m,0〈βi〈β,0〈β〈1,[B^→,T]f（x）=∫R^n（b1（x）-b1（y））…（bm（x）-bm（y））K（x-y）f（y）dy,where K is a Calder6n-Zygmund kernel. In this paper, we show that [b^→,T] is bounded from L^p（R^n） to Fp^β,∞（R^n）,as well as [b^→,1α]form L^p （R^n） to Fp^β,∞（R^n）,where 1/q=1/p-α/n.

BOUNDEDNESS OF MARCINKIEWICZ INTEGRAL RELATED TO MULTILINEAR COMMUTATORS WITH VARIABLE KERNELS ON HARDY SPACES

Let b = （b1 ,b2,… ,bm）,bi ∈∧βi（R^n）, 1 ≤ i≤ m,βi 〉 0, m∑i=1βi = β,0 〈 β 〈 1 μΩ,b （f）（x） =（∫0^∞｜Fb,t （f） （x）｜^2 dt/t^3）^1/2,Fb,t（f）（x）= ∫｜x-y｜≤t Ω（x,x-y）/｜x-y｜^n-1 m∏i=1[bi（x）-bi（t）]f（y）cy.We consider the boundedness of μΩ,b on Hardy type space Hp/b（R^n）

Multilinear Commutators of θ-Type Calderón-Zygmund Operators on Non-Homogeneous Metric Measure Spaces

In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO（μ） functions on non-homogeneous metric measure spaces is obtained.

Multilinear Commutators of Sublinear Operators on Triebel-Lizorkin Spaces

In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.

Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integral

Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1.

Multilinear Singular Integral Operators with Generalized Kernels and Their Multilinear Commutators

In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calder6n-Zygmund operators and multilinear Calderon-Zygmund operators with Dini type kernels.

Boundedness for Multilinear Commutators of Bochner-Riesz Operator

In this paper,the boundedness for the multilinear commutators of Bochner-Riesz operator is considered.We prove that the multilinear commutators generated by Bochner-Riesz operator and Lipschitz function are bounded from Lp（Rn）into ∧˙（β-np）（Rn）and from Lnβ（Rn）into BMO（Rn）.

Weak Type Weighted Inequalities for the Commutators of the Multilinear Calderón-Zygmund Operators

For the commutators of multilinear Calder ′on-Zygmund singular integral operators with B MO functions, the weak type weighted norm inequalities with respect to A^P weights are obtained.

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.

Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces

Let 6=(bi,b2,...,bm)be a collection of locally integrable functions and T,the com-mutator of multilinear singular integral operator T.Denote by L(δ)and L(δ(·))the Lipschitz spaces and the variable Lipschitz spaces,respectively.The main purpose of this paper is to establish some new characterizations of the(variable)Lipschitz spaces in terms of the boundedness of multilinear commutator T∑b in the context of the variable exponent Lebesgue spaces,that is,the authors give the necessary and sufficient conditions for bj(j=1,2,...,m)to be L(δ)or L(δ(·))via the boundedness of multilinear commutator from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces.The authors do so by applying the Fourier series technique and some pointwise esti-mate for the commutators.The key tool in obtaining such pointwise estimate is a certain generalization of the classical sharp maximal operator.

多线性交换子在变指数Herz空间上的有界性

We consider multilinear commutators of singular integrals de ned by T→bf(x)=∫R^(n)mПi=1(bi(x)-bi(y))K(x,y)f(y)dy,where K is a standard Calderon-Zygmund kernel,m is a positive integer and~b=(b_(1);b_(2);…;b_(m))is a family of m locally integrable functions.Based on the theory of variable exponent and on generalization of the BMO norm,we prove the boundedness of multilinear commutators T_(b) on grand variable Herz spaces.The result is still new even in the special case of m=1.

Boundedness of Some Operators and Commutators in Morrey-Herz Spaces on Non-Homogeneous Spaces

The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.