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.

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.

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.

Multipliers of Hardy Spaces

本文刻划了Hardy空间H^p（1≤p≤∞）到Bloch空间的乘子，推广了前人的结果。

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.

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.

ATOMIC DECOATOMIC DECOMPOSITIONS AND DUALS OF WEAK HARDY SPACES OF B-VALUED MARTINGALES

In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.

Integrability of the general product Hardy operators on the product Hardy spaces

In this paper,we prove that the general product Hardy operators are bounded from the product Hardy space H1n（Rm1×···×Rmn） to L1（R（∑ni=1mi）.

Weighted Composition Operators between Hardy Spaces on the Unit Ball

We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.

Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales

The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.

COLLECTIVELY COMPACT COMPOSITION OPERATOR SEQUENCES BETWEEN BERGMAN AND HARDY SPACES

This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces. Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions for composition operator sequences to be collectively compact between weighted Bergman spaces are given

MIXED HARDY SPACES AND THEIR APPLICATIONS

Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's identity.As an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.

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 Hausdorff operators on the power weighted Hardy spaces

In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H;（R;） （ -1 ≤α≤0）, defined by H;f（x）=∫R;Φ（u）f(A（u）x)du,where Φ∈L;oc;（R;）,A（u） = (α;（u）);is a 2×2 matrix, and each α;is a measurablefunction.We obtain that HΦ,A is bounded from H;（R;） （ -1≤α≤0） to itself, if∫R2|Φ（u）‖det A;（u）|‖A（u）‖;ln(1+‖A;（u）‖;/|det A;（u）|)du<∞.This result improves some known theorems, and in some sense it is sharp.

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHRDINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.

FRACTIONAL INTEGRALS WITH VARIABLE KERNELS ON HARDY SPACES

The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.

Boundedness of Caldero'n-Zygmund operators in product Hardy spaces

By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.

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.