BOUNDEDNESS OF COMMUTATORS FOR MARCINKIEWICZ INTEGRALS ON WEIGHTED HERZ-TYPE HARDY SPACES

In this paper, the authors study the boundedness of the operator μ^bΩ, the commutator generated by a function b ∈Lipβ （R^n） （0 〈β 〈 1） and the Marcinkiewicz integral μΩ on weighted Herz-type Hardy spaces.

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）

THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES

This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).

BOUNDEDNESS OF HIGHER ORDER COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON HARDY SPACES

Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.

BOUNDEDNESS OF COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON WEIGHTED HERZ-TYPE HARDY SPACES

In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.

BOUNDEDNESS OF COMMUTATORS RELATED TO MARCINKIEWICZ INTEGRALS ON HARDY TYPE SPACES

In this paper, the authors study the boundedness of the operator [μΩ,b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω ∈ Lipα(Sn-1)(0 <α≤ 1).

Boundedness of parammetric Marcinkiewicz integrals on weighted Hardy spaces

In this paper, several new results on the boundedness of parammetric Marcinkiewicz integrals on the weighted Hardy spaces and the weak weighted Hardy spaces are established.

Some Properties of Marcinkiewicz Integral on Herz-type Hardy Spaces

It provides the boundary proof of Marcnkiewicz integral μ Ω(f)(x) on Herz_type Hardy spaces. That is: if n(1-1q)≤α【n(1-1q)+β then μ Ω(f)(x) is boundendess from H K· α,p q(R n) to K· α,p q(R n); if α=n(1-1q)+β then μ Ω(f)(x) is boundedness from H K· α,p q(R n) to W K· α,p q(R n).

BOUNDEDNESS OF MARCINKIEWICZ INTEGRAL ON THE WEIGHTED HERZ-TYPE HARDY SPACES

In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from HKq^a、P（ω1;ω2） into Kq^a、p （ω1; ω2）.

Commutator of Marcinkiewicz Integral Operators on Herz-Morrey-Hardy Spaces with Variable Exponents

In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [b,μΩ] and obtain the result with Lipschitz function and BMO function f on the Herz-Morrey-Hardy spaces with variable exponents .

Boundedness for Multilinear Commutators of Marcinkiewicz Integral on Morrey-Herz Spaces with Non Doubling Measures

In this paper, the authors establish the boundedness of multilinear commutators generated by a Marcinkiewicz integral operator and a RBMO（μ） function on homogeneous Morrey-Herz spaces with non doubling measures.

Estimates for parametric Marcinkiewicz integrals in BMOand Campanato spaces

In this paper, the authors consider the behaviors of a class of parametricMarcinkiewicz integrals μ_Ω~ρ, μ_（Ω,）^（＊,）~ρ_λ and μ_Ω~ρ,S on BMO（Rn） and Campanato spaces with com-plex parameter ρ and the kernel Ω in Llog~＋ L（S^（n-1））. Here μ_（Ω,）^（＊,）~ρ_λand μ_Ω~ρ,S are parametricMarcinkiewicz functions corresponding to the Littlewood-Paley g_λ~＊-function and the Lusin areafunction S, respectively. Under certain weak regularity condition on Ω, the authors prove thatif f belongs to BMO（Rn） or to a certain Campanato space, then [μ_（Ω,）^（＊,）~ρ_λ（f）]~2, [μ_Ω~ρ,_S（f）]~2 and[μ_Ω~ρ（f）]~2 are either infinite everywhere or finite almost everywhere, and in the latter case, somekind of boundedness are also established.

Boundedness of Some Commutators of Marcinkiewicz Integrals on Hardy Spaces

Based on the results of the boundedness ofµ^(b)_(Ω)on L^(p) spaces,by using the theory of atomic decomposition of Hardy spaces,we obtain the boundedness ofµ^(b)_(Ω)on Hardy spaces.

BOUNDEDNESS OF GENERALIZED HIGHER COMMUTATORS OF MARCINKIEWICZ INTEGRALS

Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.

Boundedness of Some Marcinkiewicz Integral Operators Related to Higher Order Commutators on Hardy Spaces

In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ（R^n）（0 〈β≤ 1/m） and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on the Hardy type spaces Hb^m^p,n（R^n） and the Herz Hardy type spaces Hbm Kq^α,p（R^b）.

WEIGHTED BOUNDEDNESS OF PARAMETRIC MARCINKIEWICZ INTEGRAL AND HIGHER ORDER COMMUTATOR

In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and its commutator with different weight functions and Dini kernel are also discussed.

Boundedness of Hyper-Singular Parametric Marcinkiewicz Integrals with Variable Kernels

In this article, we consider the boundedness of? on Hardy type space? .

Multiple parametric Marcinkiewicz integrals with mixed homogeneity along surfaces

In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.

L^p Boundedness of Commutators of Calderón-Zygmund Singular Integral Operators

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BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL INTEGRATI ON ONHERZ-TYPE SPACES

This paper establishes some strong type and weak type estimates for commutator [b,I1] on Herz-type spaces, where b E BMO(Rn) and I1 is a fractional integration with O < l < n.