Multilinear singular and fractional integrals on weighted Hardy spaces

In this paper the boundedness properties of multilinear singular and fractional integrals on the weighted Hardy spaces are studied.

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.

Riesz Transforms Associated with Schrdinger Operators Acting on Weighted Hardy Spaces

Let L = -△＋V be a Schrodinger operator acting on L^2（R^n）, n ≥ 1, where V ≠ 0 is a nonnegative locally integrable function on R^n. In this article, we will introduce weighted Hardy spaces Hp （w） associated with L by means of the square function and then study their atomic decomposition theory. We will also show that the Riesz transform △↓L^-1/2 associated with L is bounded from our new space HP（w） to the classical weighted Hardy sp ace HP （ w ） when n / （n ＋ 1 ） 〈 p 〈 1 and w ∈ A 1 ∩ R H（ 2 / p ）＇.

A New Estimate for Bochner–Riesz Operators at the Critical Index on Weighted Hardy Spaces

Let w be a Muckenhoupt weight and Hwp （JRn） be the weighted Hardy space. In this paper, by using the atomic decomposition of Hwp（Rn）, we will show that the Bochner-Riesz operators TRδ are bounded from Hwp（Rn） to the weighted weak Hardy spaces WHwp （Rn） for 0 〈 p 〈 1 and δ = n/p- （n ＋ 1）/2. This result is new even in the unweighted case.

COMPOSITION OPERATORS BETWEEN SOME WEIGHTED HARDY SPACES

Let D be the unit disc and H（D） be the set of all analytic functions on D. In [2], C. Cowen defined a space H = f ∈ H（D） ： f（z） =sum from k=o to ∞ ak（z ＋ 1）k, z ∈ D, ‖f‖2 = sum from k=o to ∞ ｜ak｜24k ∞In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.

Weighted Composition Operators That Preserve Frames On Weighted Hardy Spaces

In this paper, we characterize weighted composition operators that preserve frames on the weighted Hardy spaces in the unit disk. In particular, we obtain the symbol properties of the bounded invertible weighted composition operators. Moreover, we establish the equivalence between bounded invertible operators and frame-preserving operators. Furthermore, we show that weighted composition operator preserves frames if and only if it preserves the Riesz bases property. Additionally,we investigate the weighted composition operators that preserve tight or normalized tight frames on the Dirichlet space.

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.

The Interpolation of Operators between Weighted Hardy Spaces and Weighted L^p Spaces

The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.

The CalderSn-Zygmund Decomposition and Interpolation on Weighted Hardy Spaces

We apply discrete Littlewood Paley Stein theory, developed by Han and Lu, to establish Calderon Zygmund decompositions and interpolation theorems on weighted Hardy spaces Hp for w C A∞ in both the one-parameter and two-parameter cases.

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.

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. -

The characterization of weighted local hardy spaces on domains and its application

In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on Lipschitz domains. Also, we give their application for the harmonic function defined in bounded Lipschitz domains.

Boundedness of Area Functions Related to Schrodinger Operators and Their Commutators in Weighted Hardy Spaces

In this paper,we consider the area function SQ related to the Schrodinger operator ■ and its commutator SQ,b´establish the boundedness of SQ from Hp(w)to L^(p)_(ρ)(w)to L^(p)(w)or WL^(p)(w),as well as the boundedness of SQ,b´from H^(1)_(ρ)(w)to WL^(1)(w).

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 Calderdn-Zygmund operator on weighted 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）.

Boundedness of Multilinear Oscillatory Singular Integral on Weighted Weak Hardy Spaces

In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH;（R;） to the weighted weak Lebesgue space WL;（R;） for ω∈A;（R;）.

Maximal Operators of Multilinear Singular Integrals on Weighted Hardy Type Spaces

In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.

Weighted Boundedness of Commutators of Generalized Calderón-Zygmund Operators

[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip;（R;）,（0 <β≤1） and T is aθ（t）-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f（x）=b（x）Tf（x）-T（bf）(x)=∫k（x,y）(b（x）-b（y）)f（y）dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H;（ω;） to L;（ω;）, and from HK;(ω;,ω;) to K;(ω;,ω;). The results extend and generalize the well-known ones in [7].

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）.