THE WEIGHTED HERZ-TYPE HARDY SPACES hK_q^(α,p)(ω_1,ω_2)

Let (.the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces (w2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish the boundedness on these spaces of the pseudo-differential operators of order zero and show that , the class of C(Rn)-functions with compactly support, is dense in and there is a subsequence, which converges in distrbutional sense to some distribution of , of any bounded sequence in In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.

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 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）.

Herz-type Hardy Space Estimates for Multilinear Operators with Dini Kernels

In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.

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 for Commutators of Calderón-Zygmund Operator on Herz-Type Hardy Space with Variable Exponent

Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.

Boundedness of the θ-type Calderón-Zygmund Operators on Weighted Herz-type Hardy Spaces

In this paper,we will discuss the boundedness of θ-type Calderón-Zygmund operator on weighted Herz-type Hardy spaces.

Some Characterizations of Weighted Herz-type Hardy Spaces and Their Applications

In this paper,the authors first establish some new real-variable characterizations of Herz- type Hardy spaces Hqα,p（ω1;ω2）and HKqα,P（ω1;ω2）,where ω1,ω2 ∈A1-weight,1【q【∞, n（1-1/q）≤α【∞ and 0【p【∞.Then,using these new characterizations,they investigate the convergence of a bounded set in these spaces,and study the boundedness of some potential operators on these spaces.

Remarks on Herz-Type Hardy Spaces Dedicated to Professor Kozo Yabuta on the occasion of his 60th birthday

Basic properties of the Herz-type Hardy spaces HKqa,p, such as the boundedness of singular integral operators and the fractional integration operators, atomic decomposition, dense subspaces, etc., are established in the full range 0【q【∞.

Bilinear Operators on Herz-type Hardy Spaces on Locally Compact Vilenkin Groups

Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B（f, g） given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Hardy space on G. And an example, the boundedness from the products of Herz space to Herz-type Hardy space is given in the last section.

BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

H■rmander's Multipliers for the Weighted Herz-type Hardy Spaces

In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2（｜x｜^t; ｜x｜^t） and HK^α,P 2（｜x｜^t; ｜x｜^t）.

The weighted Herz-type Hardy space and its applications

A certain weighted Herz-type Hardy space is introduced and its atom-decomposition theory is established. As applications of this theory, a boundedness theorem of sublinear operators and an interpolation theorem of linear operators on these spaces are given.

Herz-type Hardy spaces on Vilenkin groups and their applications

Let l ≤ q ≤ ∞, 1 - 1/q≤∞,0【p≤∞ and G be a locally compact Vilenkin group. The authors first introduce the general Herz-type Hardy spaces HKqa,p( G) and hkaq,p( G), then pre-sent the central atom or the central block and atom decompositions of these spaces. Using this charac-terization, they discuss some properties of these spaces and investigate the boundedness on the spaces Hkaq,p( G) of the fractional integral operators and the boundedness on the spaces hkaq,p( G) of the pseudo-differential operators of order zero.

Boundedness of Multilinear Operators in Herz-type Hardy Space

Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on Rn are bounded from H Kqlαl·pl（Rn）×…×HKqkαk,pk（Rn）into HKqα,p（Rn）if they have vanishing moments up to a certain order dictated by the target spaces.These conditions on vanishing moments satisfied by the multilinear operators are also necessary when αj（?）0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.

Strongly Singular Convo1ution Operators on the Weighted Herz-Type Hardy Spaces

Let 0【p≤1q【0, and w1, w2 ∈A1 （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HKqα,p（w1; w2） to the homogeneous weighted Herz spaces Kqα,p（w1;w2）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HKqα,p（w1, w2） is also investigated.

Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces

We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator.

Linear operators on weighted Herz-type Hardy spaces

Soria and Weiss extended a Stein’s result,the boundedness of singular integral op-erators on the weighted spaces L^p(w) with power weights w, to more general cases wheresingular integral operators were replaced by sublinear operators T satisfying the size condi-tion (for compact supported function f)