Boundedness of Fractional Integral with Variable Kernel and Their Commutators on Variable Exponent Herz Spaces

In this paper, we study the boundedness of the fractional integral operator and their commutator on Herz spaecs with two variable exponents . By using the properties of the variable exponents Lebesgue spaces, the boundedness of the fractional integral operator and their commutator generated by Lipschitz function is obtained on those Herz spaces.

ROUGH OPERATORS AND COMMUTATORS ON HOMOGENEOUS WEIGHTED HERZ SPACES

The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.

Boundedness for Hardy Type Operators on Herz Spaces with Variable Exponents

In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.

Vector-valued Inequalities for Commutators of Singular Integrals on Herz Spaces with Variable Exponents

Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are variable exponents.Furthermore, we show that a wide class of commutators generated by BMO functions and sublinear operators satisfy vector-valued inequalities.

Boundedness of Rough Operators on Grand Variable Herz Spaces

In this paper, we prove the boundedness of Calderón-Zygmund singular integral operators TΩ on grand Herz spaces with variable exponent under some conditions.

CBMO ESTIMATES FOR MARCINKIEWICZ INTEGRALS ON HOMOGENEOUS MORREY-HERZ SPACES

The boundedness of the commutator μΩ,b generalized by Marcinkiewicz integral μΩ and a function b（x） ∈ CBMOq （Rn） on homogeneous Morrey-Herz spaces is established.

Parameterized Littlewood-Paley Operators on Weighted Herz Spaces

The strong type and weak type estimates of parameterized Littlewood-Paley operators on the weighted Herz spaces Kq α,p（ω1,ω2） are considered. The boundednessof the commutators generated by BMO functions and parameterized Littlewood-Paley operators are also obtained.

Commutators of Littlewood-Paley Operators on Herz Spaces with Variable Exponent

Let Ω ∈ L^2（S^n-1） be homogeneous function of degree zero and b be BMO functions. In this paper, we obtain some boundedness of the Littlewood-Paley Opera- tors and their higher-order commutators on Herz spaces with variable exponent.

Multilinear Fractional Integrals and Commutators on Generalized Herz Spaces

Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα,m and Iα,m^∏b on generalized Herz spaces with general Muckenhoupt weights.

BOUNDEDNESS OF MULTILINEAR OPERATORS WITH ROUGH KERNEL ON HERZ SPACES

In this paper,the boundedness of the multilinear operators with rough kernel on the Herz-type spaces is discussed.It is proved that M A,Ω,T A,Ω are bounded on α,p q(Rn) while Mλ A,Ω,TL A,Ω are bounded from α,p 1 q 1(Rn) to α,p 2 q 2(Rn),respectively.

New Hardy Spaces Associated with Herz Spaces and Beurling Algebras on Homogeneous Groups

The author introduces the Hardy spaces associated with the Herz spaces and the Beurling algebras on homogeneous groups and establishes their atomic decomposition characterizations. As the applications of this decomposition, the duals of these Hardy spaces and the boundedness of the central δ-Calderon-Zygmund operators on these Hardy spaces are studied.

Boundedness of commutators on homogeneous Herz spaces

The boundedness on homogeneous Herz spaces is established fo r a large class of linear commutators generated by BMO(R+n) functions and linear operators of rough kernels which include the CaldernZygmund oper ators and the RicciStein oscillatory singular integrals with rough kernels.

Boundedness for multilinear fractional integral operators on Herz type spaces

In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.

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.

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.

Commutators of Bilinear Hardy Operators on Two Weighted Herz Spaces with Variable Exponents

In this paper,we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of two weighted Herz spaces.

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.

CALDER6N-ZYGMUND OPERAORS ON THE HARDY SPACES OF WEIGHTED HERZ TYPE

Applying the decomposition theorems in [1] and [2] , we obtain the boundedness theorem of Calderbn-Zygmund operator of type 6 on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. -

Boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents

We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^(˙α(⋅))_(p(⋅),q(⋅)),such as some sublinear operators,the fractional integral and its commutator.

A NOTE TO OSCILLATORY SINGULAR INTEGRALS ON HERZ-TYPE SPACES

In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Herz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions.