BOUNDEDNESS OF VECTOR-VALUED CALDERN-ZYGMUND OPERATORS ON HERZ SPACES WITH NON-DOUBLING MEASURES

In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular, we obtain vector-valued inequalities for CZO on L^q（R^d,｜x｜^α d μ）space, with 1〈q〈∞,-n〈α〈n（q-1）,and on L^1,∞ （R^d,｜x｜^α d μ）space,with -n〈α〈0.

Iterated Commutators for Multilinear Singular Integral Operators on Morrey Space with Non-Doubling Measures

Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.

TWO GENERALIZATIONS OF HARDY-LITTLEWOOD MAXIMAL OPERATOR

Two generalizations of Hardy-Littlewood maximal operator are considered. Some estimates for them are obtained.

Boundedness of Multilinear Singular Integrals and Their Commutators on Morrey-Herz Spaces with Non-doubling Measures

Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.

On the Maximal Operator Associated with Certain Rotational Invariant Measures

The aim of this work is to investigate the integrability properties of the maximal operator Mu,associated with a non-doubling measure μ defined on Rn. We start by establishing for a wide class of radial and increasing measures μ that Mu is bounded on all the spaces Lu^p（R^n）,P〉1.Also,we show that there is a radial and increasing measure p for which Mμ does not map Lμ^p（R^n） into weak Lμ^p（R^n）,1≤p〈∞.

Boundedness of Some Maximal Commutators in Hardy-type Spaces with Non-doubling Measures

Let μ be a non-negative Radon measure on R^d which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of maximal Calderón-Zygmund operators and maximal commutators which are variants of the usual maximal commutators generated by Calder6ón- Zygmund operators and RBMO（μ） functions, where the Hardytype spaces are some appropriate subspaces, associated with the considered RBMO（μ） functions, of the Hardv soace H^I（μ） of Tolsa.

Weighted estimates for commutators of singular integral operators with non-doubling measures

Letμbe a nonnegative Radon measure on R^d which only satisfiesμ(B(x,r))≤C_0r^n for all x∈R^d,r>0,and some fixed constants C_0>0 and n∈(0,d].In this paper,some weighted weak type estimates with A_(p,(log L)~σ)~ρ(μ) weights are established for the commutators generated by Calder■n-Zygmund singular integral operators with RBMO(μ) functions.

Θ-type Calderón-Zygmund Operators with Non-doubling Measures

Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ（B（x,r）） ≤ Urn for all x∈Rd, r 〉 0 and for some fixed 0 〈 n 〈 d. In this paper, under this assumption, we prove that 0-type Calder6n-Zygmund operator which is bounded on L2 （μ） is also bounded from L^∞（μ） into RBMO （μ） and from Hb （μ） into L1（μ）. According to the interpolation theorem introduced by Tolsa, the LP（μ）-boundedness （1 〈 p 〈 ∞） is established for θ-type Calder6n-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type CMderθn-Zygmundoperator with RBMO （μ） function are bounded on LP（μ） （1 〈 p 〈 ∞）.

Weighted Inequalities for the Generalized Maximal Operator in Martingale Spaces

The generalized maximal operator .44 in martingale spaces is considered. For 1 〈 p ≤ q 〈 ∞, the authors give a necessary and sufficient condition on the pair （μ, v） for M to be a bounded operator from martingale space L^P（μ） into L^q（μ） or weak-L^q（μ）, where μ is a measure on Ω × N and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed.

Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures

The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ) functions of Tolsa with non-doubling measures is obtained, provided that ∥μ∥ = ∞ and multilinear singular integrals are bounded from L 1(μ) × L 1(μ) to L 1/2,∞(μ).

ENDPOINT ESTIMATE FOR MAXIMAL COMMUTATORS WITH NON-DOUBLING MEASUES

The authors establish the weak type endpoint estimate for the maximal commutators generated by Calderon-Zygmund singular integrals and Orlicz type functions with non-doubling measures.

Atomic Hardy-type Spaces between H1 and L1 on Metric Spaces with Non-doubling Measures

Let （y, d, dλ） be （Rn, ｜·｜,μ）, where ｜·｜ is the Euclidean distance, μ is a nonnegative Radon measure on Rn satisfying the polynomial growth condition, or the Gauss measure metric space （Rn, ｜·｜,dγ）, or the space （S, d, p）, where S - Rn×R＋ is the （ax ＋ b）-group, d is the left-invariant Riemannian metric and p is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces {Xs（Y））0〈s≤∞ and the BM0-type spaces {BM0（y, s）}0〈s≤∞. Let Hi（Y） be the known atomic Hardy space and L01（y） the subspace of f ∈ L1（Y） with integral 0. The authors prove that the dual space of Xs（Y） is SM0（Y,s） when s∈ （0, ∞）, Xs（Y） = H1（Y） when s ∈ （0, 1], and X∞（y） = L01（Y） （or L1（Y））. As applications, the authors show that if T is a linear operator bounded from H1 （Y） to L1 （Y） and from L1（y） to L1,∞（Y）, then for all r ∈ （1, ∞） and s ∈ （r, ∞], T is bounded from Xr（y） to the Lorentz space L1,8（y）, which applies to the Calderon-Zygmund operator on （Rn, ｜·｜,μ）, the imaginary powers of the 0rnstein-Uhlenbeck operator on （Rn, ｜·｜,dγ） and the spectral operator associated with the spectral multiplier on （S, d, p）. All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces.

CONVERGENCE OF INVARIANT MEASURES FOR MULTIVALUED STOCHASTIC DIFFERENTIAL EQUATIONS

This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.

Singular Measures and Convolution Operators

We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type （1, 1） inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension.

极大算子及其交换子在齐次树上的加权估计

在齐次树中考虑一类测度,它到原点的距离是指数递减的.给出齐次树中关于这类测度的Lebesgue空间、 BMO(bounded mean oscillation)空间、极大算子及其交换子的定义,并利用齐次树的分解理论,证明极大算子及其交换子在Lebesgue空间的有界性及一些等价性质.

非齐型空间上奇异积分算子加权估计

让μ是Rd上非双倍的Radon测度,μ仅满足增长性条件,即存在c0>0,对所有x∈Rd,r>0,μ(B(x,r))≤c0rn成立,其中0<n≤d。学习在非双倍测度的条件下,具有Dini核的极大奇异积分算子是从L1( ω)到L1,∞( ω)和Lp( ω)有界的,其中1<p<∞,( ω)∈Ap。

算子族的点态收敛性

利用极大算子的弱型性质证明抽象空间中的算子族｛Ｔ_ε｝（ε＞０）的几乎处处收敛性定理。这些定理是推导Ｆｏｕｒｉｅｒ分析中许多算子列点态收敛性的基础．

一类极大算子的加权范数不等式

本文利用Fourier变换方法和变测度内插定理研究一类极大算子的加权范数不等式,解决了Watson,D,K.在[6]中提出的问题。

粗糙核极大函数的双权弱型不等式

本文研究了粗糙核分数型极大函数双权弱型不等式的等价特征,是已有结果的实质性改进。

通过六比特最大纠缠态来分裂量子信息(英文)

量子信息分裂或量子态共享是经典秘密共享方案在量子方案中的概括。在量子信息分裂中,一种量子态的形式被划分并分发给多个接收者。提出一个通过使用六粒子的最大纠缠态作为量子通道来分裂两量子比特混态的方案。首先Alice执行两个Bell基测量并且宣布测量结果,同时分配Charlie(Bob)来重建未知的初态。如果控制者Bob(Charlie)同意帮助Charlie(Bob)获得初态,他们就在各自的量子比特上执行单粒子测量。在发送者对粒子执行Bell基测量以及合作者对粒子执行单粒子测量之后,通过运用适当的幺正算符,接收者可以重建发送者信息的初始状态。